```
----
4D
----
```

or by complexity (only including stary cases for quasiregular linear diagrams)
or by similarity.

### Terse Overview

Indepted to the mere quantity of cases the following overview table links to additional pages too; only parts are listed in details below.

 Linear Dynkin Graphs Tridental Dynkin Graphs Loop-n-Tail Dynkin Graphs Loop Dynkin Graphs Two-Loop Dynkin Graphs Simplical Dynkin Graphs Others ``` o-P-o-Q-o-R-o ``` ```o-P-o-Q-o *b-R-o = o_ -P_ >o---R---o _Q- o- ``` ```o-P-o-Q-o-R-o-S-*b = o_ | -Q_ R >o---P---o | _S- o- ``` ```o-P-o-Q-o-R-o-S-*a = o---P---o | | S Q | | o---R---o ``` ```o-P-o-Q-o-R-o-S-*a-T-*c = _o_ _P- | -S_ o< T >o -Q_ | _R- -o- ``` ```o-P-o-Q-o-R-o-S-*a-T-*c *b-U-*d = o / T \ P _o_ S /_Q R_\ o-----U-----o ```

In the following symmetry listings "etc." means replacments according to 33/2, to 44/3, to 55/4, or to 5/25/3.

Polychora with Grünbaumian elements so far are not investigated any further. Those are Grünbaumian a priori, usually because of some subgraph -x-n/d-x-, where d is even. Others, which come out as being Grünbaumian a posteriori will be given none the less.

*) not even a scaliform representation does exist, just occures as pure faceting
**) not uniform, but at least scaliform

 loop-n-tail ones ```o-P-o-Q-o-R-o-S-*b = o_ | -Q_ R >o---P---o | _S- o- ```

### Pentachoral ("pentic") Symmetries   (up)

 o3o3o3/2o3*b (µ=2) o3o3o3o3/2*b (µ=3) o3/2o3o3o3/2*b (µ=7) quasiregulars ```x3o3o3/2o3*b - 2pen (?) (contains "2tet" as verf) o3x3o3/2o3*b - (contains "2tet") o3o3x3/2o3*b - (contains "2tet") ``` ```x3o3o3o3/2*b - 2pen (?) (contains "2tet" as verf) o3x3o3o3/2*b - (contains "2tet") o3o3x3o3/2*b - (contains "2tet") o3o3o3x3/2*b - (contains "2tet") ``` ```x3/2o3o3o3/2*b - 2pen (?) (contains "2tet" as verf) o3/2x3o3o3/2*b - (contains "2tet") o3/2o3x3o3/2*b - (contains "2tet") o3/2o3o3x3/2*b - (contains "2tet") ``` otherWythoffians ```x3x3o3/2o3*b - (contains "2tet") x3o3x3/2o3*b - (contains "2tet") o3x3x3/2o3*b - rawvtip o3o3x3/2x3*b - [Grünbaumian] x3x3x3/2o3*b - pittip x3o3x3/2x3*b - [Grünbaumian] o3x3x3/2x3*b - [Grünbaumian] x3x3x3/2x3*b - [Grünbaumian] ``` ```x3x3o3o3/2*b - (contains "2tet") x3o3x3o3/2*b - (contains "2tet") x3o3o3x3/2*b - (contains "2tet") o3x3x3o3/2*b - rawvtip o3x3o3x3/2*b - [Grünbaumian] o3o3x3x3/2*b - duhd x3x3x3o3/2*b - pittip x3x3o3x3/2*b - [Grünbaumian] x3o3x3x3/2*b - o3x3x3x3/2*b - [Grünbaumian] x3x3x3x3/2*b - [Grünbaumian] ``` ```x3/2x3o3o3/2*b - [Grünbaumian] x3/2o3x3o3/2*b - (contains "2tet") x3/2o3o3x3/2*b - (contains "2tet") o3/2x3x3o3/2*b - rawvtip o3/2x3o3x3/2*b - [Grünbaumian] o3/2o3x3x3/2*b - duhd x3/2x3x3o3/2*b - [Grünbaumian] x3/2x3o3x3/2*b - [Grünbaumian] x3/2o3x3x3/2*b - o3/2x3x3x3/2*b - [Grünbaumian] x3/2x3x3x3/2*b - [Grünbaumian] ``` (partial)snubs andholosnubs ```... ``` ```... ``` ```... ``` o3/2o3o3/2o3*b (µ=8) o3o3/2o3/2o3/2*b (µ=12) o3/2o3/2o3/2o3/2*b (µ=18) quasiregulars ```x3/2o3o3/2o3*b - 2pen (?) (contains "2tet" as verf) o3/2x3o3/2o3*b - (contains "2tet") o3/2o3x3/2o3*b - (contains "2tet") ``` ```x3o3/2o3/2o3/2*b - 2pen (?) (contains "2tet" as verf) o3x3/2o3/2o3/2*b - (contains "2tet") o3o3/2x3/2o3/2*b - (contains "2tet") ``` ```x3/2o3/2o3/2o3/2*b - 2pen (?) (contains "2tet" as verf) o3/2x3/2o3/2o3/2*b - (contains "2tet") o3/2o3/2x3/2o3/2*b - (contains "2tet") ``` otherWythoffians ```x3/2x3o3/2o3*b - [Grünbaumian] x3/2o3x3/2o3*b - (contains "2tet") o3/2x3x3/2o3*b - rawvtip o3/2o3x3/2x3*b - [Grünbaumian] x3/2x3x3/2o3*b - [Grünbaumian] x3/2o3x3/2x3*b - [Grünbaumian] o3/2x3x3/2x3*b - [Grünbaumian] x3/2x3x3/2x3*b - [Grünbaumian] ``` ```x3x3/2o3/2o3/2*b - (contains "2tet") x3o3/2x3/2o3/2*b - (contains "2tet") o3x3/2x3/2o3/2*b - [Grünbaumian] o3o3/2x3/2x3/2*b - [Grünbaumian] x3x3/2x3/2o3/2*b - [Grünbaumian] x3o3/2x3/2x3/2*b - [Grünbaumian] o3x3/2x3/2x3/2*b - [Grünbaumian] x3x3/2x3/2x3/2*b - [Grünbaumian] ``` ```x3/2x3/2o3/2o3/2*b - [Grünbaumian] x3/2o3/2x3/2o3/2*b - (contains "2tet") o3/2x3/2x3/2o3/2*b - [Grünbaumian] o3/2o3/2x3/2x3/2*b - [Grünbaumian] x3/2x3/2x3/2o3/2*b - [Grünbaumian] x3/2o3/2x3/2x3/2*b - [Grünbaumian] o3/2x3/2x3/2x3/2*b - [Grünbaumian] x3/2x3/2x3/2x3/2*b - [Grünbaumian] ``` (partial)snubs andholosnubs ```... ``` ```... ``` ```... ```

### Tesseractic ("tessic") Symmetries – type o3o3/2o4o4*b   (up)

 o3o3/2o4o4*b (µ=3) o3o3o4/3o4*b (µ=5) o3o3o4o4/3*b (µ=11) o3/2o3/2o4o4*b (µ=13) quasiregulars ```x3o3/2o4o4*b - hex+8oct (?) (contains "oct+6{4}" as verf) o3x3/2o4o4*b - (contains "oct+6{4}") o3o3/2x4o4*b - (contains "oct+6{4}") o3o3/2o4x4*b - (contains "2cube") ``` ```x3o3o4/3o4*b - hex+8oct (?) (contains "oct+6{4}" as verf) o3x3o4/3o4*b - (contains "oct+6{4}") o3o3x4/3o4*b - (contains "oct+6{4}") o3o3o4/3x4*b - (contains "2cube") ``` ```x3o3o4o4/3*b - hex+8oct (?) (contains "oct+6{4}" as verf) o3x3o4o4/3*b - (contains "oct+6{4}") o3o3x4o4/3*b - (contains "oct+6{4}") o3o3o4x4/3*b - (contains "2cube") ``` ```x3/2o3/2o4o4*b - hex+8oct (?) (contains "oct+6{4}" as verf) o3/2x3/2o4o4*b - (contains "oct+6{4}") o3/2o3/2x4o4*b - (contains "oct+6{4}") o3/2o3/2o4x4*b - (contains "2cube") ``` otherWythoffians ```x3x3/2o4o4*b - (contains "oct+6{4}") x3o3/2x4o4*b - (contains "oct+6{4}") x3o3/2o4x4*b - (contains "2cube") o3x3/2x4o4*b - [Grünbaumian] o3x3/2o4x4*b - rawvatoth o3o3/2x4x4*b - steth x3x3/2x4o4*b - [Grünbaumian] x3x3/2o4x4*b - sichado x3o3/2x4x4*b - o3x3/2x4x4*b - [Grünbaumian] x3x3/2x4x4*b - [Grünbaumian] ``` ```x3x3o4/3o4*b - (contains "oct+6{4}") x3o3x4/3o4*b - (contains "oct+6{4}") x3o3o4/3x4*b - (contains "2cube") o3x3x4/3o4*b - (contains "2cho") o3x3o4/3x4*b - rawvatoth o3o3x4/3x4*b - gittith x3x3x4/3o4*b - (contains "2oho") x3x3o4/3x4*b - sichado x3o3x4/3x4*b - skiviphado o3x3x4/3x4*b - thatoth x3x3x4/3x4*b - thatpath ``` ```x3x3o4o4/3*b - (contains "oct+6{4}") x3o3x4o4/3*b - (contains "oct+6{4}") x3o3o4x4/3*b - (contains "2cube") o3x3x4o4/3*b - (contains "2cho") o3x3o4x4/3*b - wavitoth o3o3x4x4/3*b - steth x3x3x4o4/3*b - (contains "2oho") x3x3o4x4/3*b - gichado x3o3x4x4/3*b - gikviphado o3x3x4x4/3*b - thaquitoth x3x3x4x4/3*b - thaquitpath ``` ```x3/2x3/2o4o4*b - [Grünbaumian] x3/2o3/2x4o4*b - (contains "oct+6{4}") x3/2o3/2o4x4*b - (contains "2cube") o3/2x3/2x4o4*b - [Grünbaumian] o3/2x3/2o4x4*b - rawvatoth o3/2o3/2x4x4*b - steth x3/2x3/2x4o4*b - [Grünbaumian] x3/2x3/2o4x4*b - [Grünbaumian] x3/2o3/2x4x4*b - gikviphado o3/2x3/2x4x4*b - [Grünbaumian] x3/2x3/2x4x4*b - [Grünbaumian] ``` (partial)snubs andholosnubs ```... ``` ```... ``` ```... ``` ```... ``` o3/2o3o4o4/3*b (µ=21) o3/2o3o4/3o4*b (µ=27) o3o3/2o4/3o4/3*b (µ=45) o3/2o3/2o4/3o4/3*b (µ=67) quasiregulars ```x3/2o3o4o4/3*b - hex+8oct (?) (contains "oct+6{4}" as verf) o3/2x3o4o4/3*b - (contains "oct+6{4}") o3/2o3x4o4/3*b - (contains "oct+6{4}") o3/2o3o4x4/3*b - (contains "2cube") ``` ```x3/2o3o4/3o4*b - hex+8oct (?) (contains "oct+6{4}" as verf) o3/2x3o4/3o4*b - (contains "oct+6{4}") o3/2o3x4/3o4*b - (contains "oct+6{4}") o3/2o3o4/3x4*b - (contains "2cube") ``` ```x3o3/2o4/3o4/3*b - hex+8oct (?) (contains "oct+6{4}" as verf) o3x3/2o4/3o4/3*b - (contains "oct+6{4}") o3o3/2x4/3o4/3*b - (contains "oct+6{4}") o3o3/2o4/3x4/3*b - (contains "2cube") ``` ```x3/2o3/2o4/3o4/3*b - hex+8oct (?) (contains "oct+6{4}" as verf) o3/2x3/2o4/3o4/3*b - (contains "oct+6{4}") o3/2o3/2x4/3o4/3*b - (contains "oct+6{4}") o3/2o3/2o4/3x4/3*b - (contains "2cube") ``` otherWythoffians ```x3/2x3o4o4/3*b - [Grünbaumian] x3/2o3x4o4/3*b - (contains "oct+6{4}") x3/2o3o4x4/3*b - (contains "2cube") o3/2x3x4o4/3*b - (contains "2cho") o3/2x3o4x4/3*b - wavitoth o3/2o3x4x4/3*b - steth x3/2x3x4o4/3*b - [Grünbaumian] x3/2x3o4x4/3*b - [Grünbaumian] x3/2o3x4x4/3*b - o3/2x3x4x4/3*b - thaquitoth x3/2x3x4x4/3*b - [Grünbaumian] ``` ```x3/2x3o4/3o4*b - [Grünbaumian] x3/2o3x4/3o4*b - (contains "oct+6{4}") x3/2o3o4/3x4*b - (contains "2cube") o3/2x3x4/3o4*b - (contains "2cho") o3/2x3o4/3x4*b - rawvatoth o3/2o3x4/3x4*b - gittith x3/2x3x4/3o4*b - [Grünbaumian] x3/2x3o4/3x4*b - [Grünbaumian] x3/2o3x4/3x4*b - o3/2x3x4/3x4*b - thatoth x3/2x3x4/3x4*b - [Grünbaumian] ``` ```x3x3/2o4/3o4/3*b - (contains "oct+6{4}") x3o3/2x4/3o4/3*b - (contains "oct+6{4}") x3o3/2o4/3x4/3*b - (contains "2cube") o3x3/2x4/3o4/3*b - [Grünbaumian] o3x3/2o4/3x4/3*b - wavitoth o3o3/2x4/3x4/3*b - gittith x3x3/2x4/3o4/3*b - [Grünbaumian] x3x3/2o4/3x4/3*b - gichado x3o3/2x4/3x4/3*b - o3x3/2x4/3x4/3*b - [Grünbaumian] x3x3/2x4/3x4/3*b - [Grünbaumian] ``` ```x3/2x3/2o4/3o4/3*b - [Grünbaumian] x3/2o3/2x4/3o4/3*b - (contains "oct+6{4}") x3/2o3/2o4/3x4/3*b - (contains "2cube") o3/2x3/2x4/3o4/3*b - [Grünbaumian] o3/2x3/2o4/3x4/3*b - wavitoth o3/2o3/2x4/3x4/3*b - gittith x3/2x3/2x4/3o4/3*b - [Grünbaumian] x3/2x3/2o4/3x4/3*b - [Grünbaumian] x3/2o3/2x4/3x4/3*b - skiviphado o3/2x3/2x4/3x4/3*b - [Grünbaumian] x3/2x3/2x4/3x4/3*b - [Grünbaumian] ``` (partial)snubs andholosnubs ```... ``` ```... ``` ```... ``` ```... ```

### Tesseractic ("tessic") Symmetries – type o4o3o3/2o3*b   (up)

 o4o3o3/2o3*b (µ=2) o4o3o3o3/2*b (µ=6) o4/3o3o3o3/2*b (µ=26) quasiregulars ```x4o3o3/2o3*b - 2tes (?) (contains q-"2tet" as verf) o4x3o3/2o3*b - (contains "2tet") o4o3x3/2o3*b - (contains "2tet") ``` ```x4o3o3o3/2*b - 2tes (?) (contains q-"2tet" as verf) o4x3o3o3/2*b - (contains "2tet") o4o3x3o3/2*b - (contains "2tet") o4o3o3x3/2*b - (contains "2tet") ``` ```x4/3o3o3o3/2*b - 2tes (?) (contains q-"2tet" as verf) o4/3x3o3o3/2*b - (contains "2tet") o4/3o3x3o3/2*b - (contains "2tet") o4/3o3o3x3/2*b - (contains "2tet") ``` otherWythoffians ```x4x3o3/2o3*b - (contains "2tet") x4o3x3/2o3*b - (contains "2tet") o4x3x3/2o3*b - rawvhitto o4o3x3/2x3*b - [Grünbaumian] x4x3x3/2o3*b - siphado x4o3x3/2x3*b - [Grünbaumian] o4x3x3/2x3*b - [Grünbaumian] x4x3x3/2x3*b - [Grünbaumian] ``` ```x4x3o3o3/2*b - (contains "2tet") x4o3x3o3/2*b - (contains "2tet") x4o3o3x3/2*b - (contains "2tet") o4x3x3o3/2*b - rawvhitto o4x3o3x3/2*b - [Grünbaumian] o4o3x3x3/2*b - 2oh (?) x4x3x3o3/2*b - siphado x4x3o3x3/2*b - [Grünbaumian] x4o3x3x3/2*b - o4x3x3x3/2*b - [Grünbaumian] x4x3x3x3/2*b - [Grünbaumian] ``` ```x4/3x3o3o3/2*b - (contains "2tet") x4/3o3x3o3/2*b - (contains "2tet") x4/3o3o3x3/2*b - (contains "2tet") o4/3x3x3o3/2*b - rawvhitto o4/3x3o3x3/2*b - [Grünbaumian] o4/3o3x3x3/2*b - 2oh (?) x4/3x3x3o3/2*b - giphado x4/3x3o3x3/2*b - [Grünbaumian] x4/3o3x3x3/2*b - o4/3x3x3x3/2*b - [Grünbaumian] x4/3x3x3x3/2*b - [Grünbaumian] ``` (partial)snubs andholosnubs ```... ``` ```... ``` ```... ``` o4/3o3o3/2o3*b (µ=30) o4o3/2o3/2o3/2*b (µ=34) o4/3o3/2o3/2o3/2*b (µ=62) quasiregulars ```x4/3o3o3/2o3*b - 2tes (?) (contains q-"2tet" as verf) o4/3x3o3/2o3*b - (contains "2tet") o4/3o3x3/2o3*b - (contains "2tet") ``` ```x4o3/2o3/2o3/2*b - 2tes (?) (contains q-"2tet" as verf) o4x3/2o3/2o3/2*b - (contains "2tet") o4o3/2x3/2o3/2*b - (contains "2tet") ``` ```x4/3o3/2o3/2o3/2*b - 2tes (?) (contains q-"2tet" as verf) o4/3x3/2o3/2o3/2*b - (contains "2tet") o4/3o3/2x3/2o3/2*b - (contains "2tet") ``` otherWythoffians ```x4/3x3o3/2o3*b - (contains "2tet") x4/3o3x3/2o3*b - (contains "2tet") o4/3x3x3/2o3*b - rawvhitto o4/3o3x3/2x3*b - [Grünbaumian] x4/3x3x3/2o3*b - giphado x4/3o3x3/2x3*b - [Grünbaumian] o4/3x3x3/2x3*b - [Grünbaumian] x4/3x3x3/2x3*b - [Grünbaumian] ``` ```x4x3/2o3/2o3/2*b - (contains "2tet") x4o3/2x3/2o3/2*b - (contains "2tet") o4x3/2x3/2o3/2*b - [Grünbaumian] o4o3/2x3/2x3/2*b - [Grünbaumian] x4x3/2x3/2o3/2*b - [Grünbaumian] x4o3/2x3/2x3/2*b - [Grünbaumian] o4x3/2x3/2x3/2*b - [Grünbaumian] x4x3/2x3/2x3/2*b - [Grünbaumian] ``` ```x4/3x3/2o3/2o3/2*b - (contains "2tet") x4/3o3/2x3/2o3/2*b - (contains "2tet") o4/3x3/2x3/2o3/2*b - [Grünbaumian] o4/3o3/2x3/2x3/2*b - [Grünbaumian] x4/3x3/2x3/2o3/2*b - [Grünbaumian] x4/3o3/2x3/2x3/2*b - [Grünbaumian] o4/3x3/2x3/2x3/2*b - [Grünbaumian] x4/3x3/2x3/2x3/2*b - [Grünbaumian] ``` (partial)snubs andholosnubs ```... ``` ```... ``` ```... ```

### Icositetrachoral ("icoic") Symmetries   (up)

 o3o4o3/2o4*b (µ=2) o3o4o3o4/3*b (µ=22) o3/2o4o3/2o4*b (µ=46) quasiregulars ```x3o4o3/2o4*b - 2ico (?) (contains "2cube" as verf) o3x4o3/2o4*b - (contains "2cube") o3o4x3/2o4*b - (contains "oct+6{4}") ``` ```x3o4o3o4/3*b - 2ico (?) (contains "2cube" as verf) o3x4o3o4/3*b - (contains "2cube") o3o4x3o4/3*b - (contains "oct+6{4}") o3o4o3x4/3*b - (contains "oct+6{4}") ``` ```x3/2o4o3/2o4*b - 2ico (?) (contains "2cube" as verf) o3/2x4o3/2o4*b - (contains "2cube") o3/2o4x3/2o4*b - (contains "oct+6{4}") ``` otherWythoffians ```x3x4o3/2o4*b - (contains "2cube") x3o4x3/2o4*b - (contains "oct+6{4}") o3x4x3/2o4*b - rawvaty o3o4x3/2x4*b - [Grünbaumian] x3x4x3/2o4*b - sipti x3o4x3/2x4*b - [Grünbaumian] o3x4x3/2x4*b - [Grünbaumian] x3x4x3/2x4*b - [Grünbaumian] ``` ```x3x4o3o4/3*b - (contains "2cube") x3o4x3o4/3*b - (contains "oct+6{4}") x3o4o3x4/3*b - (contains "oct+6{4}") o3x4x3o4/3*b - rawvaty o3x4o3x4/3*b - wavaty o3o4x3x4/3*b - (contains "2cho") x3x4x3o4/3*b - sipti x3x4o3x4/3*b - gipti x3o4x3x4/3*b - o3x4x3x4/3*b - iquatoc x3x4x3x4/3*b - iquatpic ``` ```x3/2x4o3/2o4*b - [Grünbaumian] x3/2o4x3/2o4*b - (contains "oct+6{4}") o3/2x4x3/2o4*b - rawvaty o3/2o4x3/2x4*b - [Grünbaumian] x3/2x4x3/2o4*b - [Grünbaumian] x3/2o4x3/2x4*b - [Grünbaumian] o3/2x4x3/2x4*b - [Grünbaumian] x3/2x4x3/2x4*b - [Grünbaumian] ``` (partial)snubs andholosnubs ```... ``` ```... ``` ```... ``` o3/2o4o3o4/3*b (µ=74) o3o4/3o3/2o4/3*b (µ=146) o3/2o4/3o3/2o4/3*b (µ=190) quasiregulars ```x3/2o4o3o4/3*b - 2ico (?) (contains "2cube" as verf) o3/2x4o3o4/3*b - (contains "2cube") o3/2o4x3o4/3*b - (contains "oct+6{4}") o3/2o4o3x4/3*b - (contains "oct+6{4}") ``` ```x3o4/3o3/2o4/3*b - 2ico (?) (contains "2cube" as verf) o3x4/3o3/2o4/3*b - (contains "2cube") o3o4/3x3/2o4/3*b - (contains "oct+6{4}") ``` ```x3/2o4/3o3/2o4/3*b - 2ico (?) (contains "2cube" as verf) o3/2x4/3o3/2o4/3*b - (contains "2cube") o3/2o4/3x3/2o4/3*b - (contains "oct+6{4}") ``` otherWythoffians ```x3/2x4o3o4/3*b - [Grünbaumian] x3/2o4x3o4/3*b - (contains "oct+6{4}") x3/2o4o3x4/3*b - (contains "oct+6{4}") o3/2x4x3o4/3*b - rawvaty o3/2x4o3x4/3*b - wavaty o3/2o4x3x4/3*b - (contains "2cho") x3/2x4x3o4/3*b - [Grünbaumian] x3/2x4o3x4/3*b - [Grünbaumian] x3/2o4x3x4/3*b - o3/2x4x3x4/3*b - iquatoc x3/2x4x3x4/3*b - [Grünbaumian] ``` ```x3x4/3o3/2o4/3*b - (contains "2cube") x3o4/3x3/2o4/3*b - (contains "oct+6{4}") o3x4/3x3/2o4/3*b - wavaty o3o4/3x3/2x4/3*b - [Grünbaumian] x3x4/3x3/2o4/3*b - gipti x3o4/3x3/2x4/3*b - [Grünbaumian] o3x4/3x3/2x4/3*b - [Grünbaumian] x3x4/3x3/2x4/3*b - [Grünbaumian] ``` ```x3/2x4/3o3/2o4/3*b - [Grünbaumian] x3/2o4/3x3/2o4/3*b - (contains "oct+6{4}") o3/2x4/3x3/2o4/3*b - wavaty o3/2o4/3x3/2x4/3*b - [Grünbaumian] x3/2x4/3x3/2o4/3*b - [Grünbaumian] x3/2o4/3x3/2x4/3*b - [Grünbaumian] o3/2x4/3x3/2x4/3*b - [Grünbaumian] x3/2x4/3x3/2x4/3*b - [Grünbaumian] ``` (partial)snubs andholosnubs ```... ``` ```... ``` ```... ```

### Hecatonicosachoral ("hyic") Symmetries – type o3o3o3/2o5*b   (up)

 o3o3o3/2o5*b (µ=39) o3o3/2o3o5*b (µ=81) o3o3o3o5/4*b (µ=561) o3/2o3/2o3o5*b (µ=639) quasiregulars ```x3o3o3/2o5*b - gidtixhi o3x3o3/2o5*b - riggidtixhi o3o3x3/2o5*b - (contains "2gike") o3o3o3/2x5*b - giddatady ``` ```x3o3/2o3o5*b - gidtixhi o3x3/2o3o5*b - riggidtixhi o3o3/2x3o5*b - (contains "2gike") o3o3/2o3x5*b - giddatady ``` ```x3o3o3o5/4*b - gidtixhi o3x3o3o5/4*b - riggidtixhi o3o3x3o5/4*b - (contains "2gike") o3o3o3x5/4*b - giddatady ``` ```x3/2o3/2o3o5*b - gidtixhi o3/2x3/2o3o5*b - riggidtixhi o3/2o3/2x3o5*b - (contains "2gike") o3/2o3/2o3x5*b - giddatady ``` otherWythoffians ```x3x3o3/2o5*b - tiggidtixhi x3o3x3/2o5*b - (contains "2gike") x3o3o3/2x5*b - sadtef pixady o3x3x3/2o5*b - grawvixady o3x3o3/2x5*b - (contains "2seihid") o3o3x3/2x5*b - [Grünbaumian] x3x3x3/2o5*b - giphixhi x3x3o3/2x5*b - x3o3x3/2x5*b - [Grünbaumian] o3x3x3/2x5*b - [Grünbaumian] x3x3x3/2x5*b - [Grünbaumian] ``` ```x3x3/2o3o5*b - tiggidtixhi x3o3/2x3o5*b - (contains "2gike") x3o3/2o3x5*b - sadtef pixady o3x3/2x3o5*b - [Grünbaumian] o3x3/2o3x5*b - (contains "2seihid") o3o3/2x3x5*b - gohihix x3x3/2x3o5*b - [Grünbaumian] x3x3/2o3x5*b - x3o3/2x3x5*b - o3x3/2x3x5*b - [Grünbaumian] x3x3/2x3x5*b - [Grünbaumian] ``` ```x3x3o3o5/4*b - tiggidtixhi x3o3x3o5/4*b - (contains "2gike") x3o3o3x5/4*b - (contains gicdatrid) o3x3x3o5/4*b - grawvixady o3x3o3x5/4*b - [Grünbaumian] o3o3x3x5/4*b - gohihix x3x3x3o5/4*b - giphixhi x3x3o3x5/4*b - [Grünbaumian] x3o3x3x5/4*b - o3x3x3x5/4*b - [Grünbaumian] x3x3x3x5/4*b - [Grünbaumian] ``` ```x3/2x3/2o3o5*b - [Grünbaumian] x3/2o3/2x3o5*b - (contains "2gike") x3/2o3/2o3x5*b - (contains gicdatrid) o3/2x3/2x3o5*b - [Grünbaumian] o3/2x3/2o3x5*b - (contains "2seihid") o3/2o3/2x3x5*b - gohihix x3/2x3/2x3o5*b - [Grünbaumian] x3/2x3/2o3x5*b - [Grünbaumian] x3/2o3/2x3x5*b - o3/2x3/2x3x5*b - [Grünbaumian] x3/2x3/2x3x5*b - [Grünbaumian] ``` (partial)snubs andholosnubs ```... ``` ```... ``` ```... ``` ```... ``` o3/2o3o3/2o5*b (µ=681) o3/2o3o3o5/4*b (µ=1119) o3o3/2o3/2o5/4*b (µ=1719) o3/2o3/2o3/2o5/4*b (µ=2361) quasiregulars ```x3/2o3o3/2o5*b - gidtixhi o3/2x3o3/2o5*b - riggidtixhi o3/2o3x3/2o5*b - (contains "2gike") o3/2o3o3/2x5*b - giddatady ``` ```x3/2o3o3o5/4*b - gidtixhi o3/2x3o3o5/4*b - riggidtixhi o3/2o3x3o5/4*b - (contains "2gike") o3/2o3o3x5/4*b - giddatady ``` ```x3o3/2o3/2o5/4*b - gidtixhi o3x3/2o3/2o5/4*b - riggidtixhi o3o3/2x3/2o5/4*b - (contains "2gike") o3o3/2o3/2x5/4*b - giddatady ``` ```x3/2o3/2o3/2o5/4*b - gidtixhi o3/2x3/2o3/2o5/4*b - riggidtixhi o3/2o3/2x3/2o5/4*b - (contains "2gike") o3/2o3/2o3/2x5/4*b - giddatady ``` otherWythoffians ```x3/2x3o3/2o5*b - [Grünbaumian] x3/2o3x3/2o5*b - (contains "2gike") x3/2o3o3/2x5*b - (contains gicdatrid) o3/2x3x3/2o5*b - grawvixady o3/2x3o3/2x5*b - (contains "2seihid") o3/2o3x3/2x5*b - [Grünbaumian] x3/2x3x3/2o5*b - [Grünbaumian] x3/2x3o3/2x5*b - [Grünbaumian] x3/2o3x3/2x5*b - [Grünbaumian] o3/2x3x3/2x5*b - [Grünbaumian] x3/2x3x3/2x5*b - [Grünbaumian] ``` ```x3/2x3o3o5/4*b - [Grünbaumian] x3/2o3x3o5/4*b - (contains "2gike") x3/2o3o3x5/4*b - sadtef pixady o3/2x3x3o5/4*b - grawvixady o3/2x3o3x5/4*b - [Grünbaumian] o3/2o3x3x5/4*b - gohihix x3/2x3x3o5/4*b - [Grünbaumian] x3/2x3o3x5/4*b - [Grünbaumian] x3/2o3x3x5/4*b - o3/2x3x3x5/4*b - [Grünbaumian] x3/2x3x3x5/4*b - [Grünbaumian] ``` ```x3x3/2o3/2o5/4*b - tiggidtixhi x3o3/2x3/2o5/4*b - (contains "2gike") x3o3/2o3/2x5/4*b - (contains gicdatrid) o3x3/2x3/2o5/4*b - [Grünbaumian] o3x3/2o3/2x5/4*b - [Grünbaumian] o3o3/2x3/2x5/4*b - [Grünbaumian] x3x3/2x3/2o5/4*b - [Grünbaumian] x3x3/2o3/2x5/4*b - [Grünbaumian] x3o3/2x3/2x5/4*b - [Grünbaumian] o3x3/2x3/2x5/4*b - [Grünbaumian] x3x3/2x3/2x5/4*b - [Grünbaumian] ``` ```x3/2x3/2o3/2o5/4*b - [Grünbaumian] x3/2o3/2x3/2o5/4*b - (contains "2gike") x3/2o3/2o3/2x5/4*b - sadtef pixady o3/2x3/2x3/2o5/4*b - [Grünbaumian] o3/2x3/2o3/2x5/4*b - [Grünbaumian] o3/2o3/2x3/2x5/4*b - [Grünbaumian] x3/2x3/2x3/2o5/4*b - [Grünbaumian] x3/2x3/2o3/2x5/4*b - [Grünbaumian] x3/2o3/2x3/2x5/4*b - [Grünbaumian] o3/2x3/2x3/2x5/4*b - [Grünbaumian] x3/2x3/2x3/2x5/4*b - [Grünbaumian] ``` (partial)snubs andholosnubs ```... ``` ```... ``` ```... ``` ```... ```

### Hecatonicosachoral ("hyic") Symmetries – type o3o3o3o5/2*b   (up)

 o3o3o3o5/2*b (µ=9) o3/2o3o3o5/2*b (µ=231) o3o3o3/2o5/3*b (µ=591) o3o3/2o3/2o5/2*b (µ=831) quasiregulars ```x3o3o3o5/2*b - sidtixhi o3x3o3o5/2*b - rissidtixhi o3o3x3o5/2*b - (contains "2ike") o3o3o3x5/2*b - dattady ``` ```x3/2o3o3o5/2*b - sidtixhi o3/2x3o3o5/2*b - rissidtixhi o3/2o3x3o5/2*b - (contains "2ike") o3/2o3o3x5/2*b - dattady ``` ```x3o3o3/2o5/3*b - sidtixhi o3x3o3/2o5/3*b - rissidtixhi o3o3x3/2o5/3*b - (contains "2ike") o3o3o3/2x5/3*b - dattady ``` ```x3o3/2o3/2o5/2*b - sidtixhi o3x3/2o3/2o5/2*b - rissidtixhi o3o3/2x3/2o5/2*b - (contains "2ike") o3o3/2o3/2x5/2*b - dattady ``` otherWythoffians ```x3x3o3o5/2*b - tissidtixhi x3o3x3o5/2*b - (contains "2ike") x3o3o3x5/2*b - (contains sicdatrid) o3x3x3o5/2*b - swavixady o3x3o3x5/2*b - [Grünbaumian] o3o3x3x5/2*b - shihix x3x3x3o5/2*b - sphixhi x3x3o3x5/2*b - [Grünbaumian] x3o3x3x5/2*b - o3x3x3x5/2*b - [Grünbaumian] x3x3x3x5/2*b - [Grünbaumian] ``` ```x3/2x3o3o5/2*b - [Grünbaumian] x3/2o3x3o5/2*b - (contains "2ike") x3/2o3o3x5/2*b - gadtef pixady o3/2x3x3o5/2*b - swavixady o3/2x3o3x5/2*b - [Grünbaumian] o3/2o3x3x5/2*b - shihix x3/2x3x3o5/2*b - [Grünbaumian] x3/2x3o3x5/2*b - [Grünbaumian] x3/2o3x3x5/2*b - o3/2x3x3x5/2*b - [Grünbaumian] x3/2x3x3x5/2*b - [Grünbaumian] ``` ```x3x3o3/2o5/3*b - tissidtixhi x3o3x3/2o5/3*b - (contains "2ike") x3o3o3/2x5/3*b - gadtef pixady o3x3x3/2o5/3*b - swavixady o3x3o3/2x5/3*b - (contains "2geihid") o3o3x3/2x5/3*b - [Grünbaumian] x3x3x3/2o5/3*b - sphixhi x3x3o3/2x5/3*b - x3o3x3/2x5/3*b - [Grünbaumian] o3x3x3/2x5/3*b - [Grünbaumian] x3x3x3/2x5/3*b - [Grünbaumian] ``` ```x3x3/2o3/2o5/2*b - tissidtixhi x3o3/2x3/2o5/2*b - (contains "2ike") x3o3/2o3/2x5/2*b - (contains sicdatrid) o3x3/2x3/2o5/2*b - [Grünbaumian] o3x3/2o3/2x5/2*b - [Grünbaumian] o3o3/2x3/2x5/2*b - [Grünbaumian] x3x3/2x3/2o5/2*b - [Grünbaumian] x3x3/2o3/2x5/2*b - [Grünbaumian] x3o3/2x3/2x5/2*b - [Grünbaumian] o3x3/2x3/2x5/2*b - [Grünbaumian] x3x3/2x3/2x5/2*b - [Grünbaumian] ``` (partial)snubs andholosnubs ```... ``` ```... ``` ```... ``` ```... ``` o3o3/2o3o5/3*b (µ=969) o3/2o3/2o3o5/3*b (µ=1191) o3/2o3o3/2o5/3*b (µ=1569) o3/2o3/2o3/2o5/2*b (µ=1809) quasiregulars ```x3o3/2o3o5/3*b - sidtixhi o3x3/2o3o5/3*b - rissidtixhi o3o3/2x3o5/3*b - (contains "2ike") o3o3/2o3x5/3*b - dattady ``` ```x3/2o3/2o3o5/3*b - sidtixhi o3/2x3/2o3o5/3*b - rissidtixhi o3/2o3/2x3o5/3*b - (contains "2ike") o3/2o3/2o3x5/3*b - dattady ``` ```x3/2o3o3/2o5/3*b - sidtixhi o3/2x3o3/2o5/3*b - rissidtixhi o3/2o3x3/2o5/3*b - (contains "2ike") o3/2o3o3/2x5/3*b - dattady ``` ```x3/2o3/2o3/2o5/2*b - sidtixhi o3/2x3/2o3/2o5/2*b - rissidtixhi o3/2o3/2x3/2o5/2*b - (contains "2ike") o3/2o3/2o3/2x5/2*b - dattady ``` otherWythoffians ```x3x3/2o3o5/3*b - tissidtixhi x3o3/2x3o5/3*b - (contains "2ike") x3o3/2o3x5/3*b - gadtef pixady o3x3/2x3o5/3*b - [Grünbaumian] o3x3/2o3x5/3*b - (contains "2geihid") o3o3/2x3x5/3*b - shihix x3x3/2x3o5/3*b - [Grünbaumian] x3x3/2o3x5/3*b - x3o3/2x3x5/3*b - o3x3/2x3x5/3*b - [Grünbaumian] x3x3/2x3x5/3*b - [Grünbaumian] ``` ```x3/2x3/2o3o5/3*b - [Grünbaumian] x3/2o3/2x3o5/3*b - (contains "2ike") x3/2o3/2o3x5/3*b - (contains sicdatrid) o3/2x3/2x3o5/3*b - [Grünbaumian] o3/2x3/2o3x5/3*b - (contains "2geihid") o3/2o3/2x3x5/3*b - shihix x3/2x3/2x3o5/3*b - [Grünbaumian] x3/2x3/2o3x5/3*b - [Grünbaumian] x3/2o3/2x3x5/3*b - o3/2x3/2x3x5/3*b - [Grünbaumian] x3/2x3/2x3x5/3*b - [Grünbaumian] ``` ```x3/2x3o3/2o5/3*b - [Grünbaumian] x3/2o3x3/2o5/3*b - (contains "2ike") x3/2o3o3/2x5/3*b - (contains sicdatrid) o3/2x3x3/2o5/3*b - swavixady o3/2x3o3/2x5/3*b - (contains "2geihid") o3/2o3x3/2x5/3*b - [Grünbaumian] x3/2x3x3/2o5/3*b - [Grünbaumian] x3/2x3o3/2x5/3*b - [Grünbaumian] x3/2o3x3/2x5/3*b - [Grünbaumian] o3/2x3x3/2x5/3*b - [Grünbaumian] x3/2x3x3/2x5/3*b - [Grünbaumian] ``` ```x3/2x3/2o3/2o5/2*b - [Grünbaumian] x3/2o3/2x3/2o5/2*b - (contains "2ike") x3/2o3/2o3/2x5/2*b - gadtef pixady o3/2x3/2x3/2o5/2*b - [Grünbaumian] o3/2x3/2o3/2x5/2*b - [Grünbaumian] o3/2o3/2x3/2x5/2*b - [Grünbaumian] x3/2x3/2x3/2o5/2*b - [Grünbaumian] x3/2x3/2o3/2x5/2*b - [Grünbaumian] x3/2o3/2x3/2x5/2*b - [Grünbaumian] o3/2x3/2x3/2x5/2*b - [Grünbaumian] x3/2x3/2x3/2x5/2*b - [Grünbaumian] ``` (partial)snubs andholosnubs ```... ``` ```... ``` ```... ``` ```... ```

### Hecatonicosachoral ("hyic") Symmetries – type o3o3o5o3/2*b   (up)

 o3o3o5o3/2*b (µ=218) o3o3o5/4o3*b (µ=382) o3/2o3o5o3/2*b (µ=502) quasiregulars ```x3o3o5o3/2*b - 2gax (?) (contains "2gike" as verf) o3x3o5o3/2*b - (contains "2gike") o3o3x5o3/2*b - gadtaxhi o3o3o5x3/2*b - gadtaxhi ``` ```x3o3o5/4o3*b - 2gax (?) (contains "2gike" as verf) o3x3o5/4o3*b - (contains "2gike") o3o3x5/4o3*b - gadtaxhi ``` ```x3/2o3o5o3/2*b - 2gax (?) (contains "2gike" as verf) o3/2x3o5o3/2*b - (contains "2gike") o3/2o3x5o3/2*b - gadtaxhi o3/2o3o5x3/2*b - gadtaxhi ``` otherWythoffians ```x3x3o5o3/2*b - (contains "2gike") x3o3x5o3/2*b - getit phiddix x3o3o5x3/2*b - (contains "2thah") o3x3x5o3/2*b - rawvhiddix o3x3o5x3/2*b - [Grünbaumian] o3o3x5x3/2*b - (contains "2seihid") x3x3x5o3/2*b - giphiddix x3x3o5x3/2*b - [Grünbaumian] x3o3x5x3/2*b - o3x3x5x3/2*b - [Grünbaumian] x3x3x5x3/2*b - [Grünbaumian] ``` ```x3x3o5/4o3*b - (contains "2gike") x3o3x5/4o3*b - getit phiddix o3x3x5/4o3*b - rawvhiddix o3o3x5/4x3*b - [Grünbaumian] x3x3x5/4o3*b - giphiddix x3o3x5/4x3*b - [Grünbaumian] o3x3x5/4x3*b - [Grünbaumian] x3x3x5/4x3*b - [Grünbaumian] ``` ```x3/2x3o5o3/2*b - [Grünbaumian] x3/2o3x5o3/2*b - (contains "2thah") x3/2o3o5x3/2*b - getit phiddix o3/2x3x5o3/2*b - rawvhiddix o3/2x3o5x3/2*b - [Grünbaumian] o3/2o3x5x3/2*b - (contains "2seihid") x3/2x3x5o3/2*b - [Grünbaumian] x3/2x3o5x3/2*b - [Grünbaumian] x3/2o3x5x3/2*b - o3/2x3x5x3/2*b - [Grünbaumian] x3/2x3x5x3/2*b - [Grünbaumian] ``` (partial)snubs andholosnubs ```... ``` ```... ``` ```... ``` o3/2o3o5/4o3*b (µ=1298) o3o3/2o5/4o3/2*b (µ=1582) o3/2o3/2o5/4o3/2*b (µ=2498) quasiregulars ```x3/2o3o5/4o3*b - 2gax (?) (contains "2gike" as verf) o3/2x3o5/4o3*b - (contains "2gike") o3/2o3x5/4o3*b - gadtaxhi ``` ```x3o3/2o5/4o3/2*b - 2gax (?) (contains "2gike" as verf) o3x3/2o5/4o3/2*b - (contains "2gike") o3o3/2x5/4o3/2*b - gadtaxhi ``` ```x3/2o3/2o5/4o3/2*b - 2gax (?) (contains "2gike" as verf) o3/2x3/2o5/4o3/2*b - (contains "2gike") o3/2o3/2x5/4o3/2*b - gadtaxhi ``` otherWythoffians ```x3/2x3o5/4o3*b - [Grünbaumian] x3/2o3x5/4o3*b - (contains "2thah") o3/2x3x5/4o3*b - rawvhiddix o3/2o3x5/4x3*b - [Grünbaumian] x3/2x3x5/4o3*b - [Grünbaumian] x3/2o3x5/4x3*b - [Grünbaumian] o3/2x3x5/4x3*b - [Grünbaumian] x3/2x3x5/4x3*b - [Grünbaumian] ``` ```x3x3/2o5/4o3/2*b - (contains "2gike") x3o3/2x5/4o3/2*b - (contains "2thah") o3x3/2x5/4o3/2*b - [Grünbaumian] o3o3/2x5/4x3/2*b - [Grünbaumian] x3x3/2x5/4o3/2*b - [Grünbaumian] x3o3/2x5/4x3/2*b - [Grünbaumian] o3x3/2x5/4x3/2*b - [Grünbaumian] x3x3/2x5/4x3/2*b - [Grünbaumian] ``` ```x3/2x3/2o5/4o3/2*b - [Grünbaumian] x3/2o3/2x5/4o3/2*b - getit phiddix o3/2x3/2x5/4o3/2*b - [Grünbaumian] o3/2o3/2x5/4x3/2*b - [Grünbaumian] x3/2x3/2x5/4o3/2*b - [Grünbaumian] x3/2o3/2x5/4x3/2*b - [Grünbaumian] o3/2x3/2x5/4x3/2*b - [Grünbaumian] x3/2x3/2x5/4x3/2*b - [Grünbaumian] ``` (partial)snubs andholosnubs ```... ``` ```... ``` ```... ```

### Hecatonicosachoral ("hyic") Symmetries – type o3o3o5/2o3*b   (up)

 o3o3o5/2o3*b (µ=2) o3/2o3o5/2o3*b (µ=238) o3o3o5/3o3/2*b (µ=598) quasiregulars ```x3o3o5/2o3*b - 2ex (?) (contains "2ike" as verf) o3x3o5/2o3*b - (contains "2ike") o3o3x5/2o3*b - sidtaxhi ``` ```x3/2o3o5/2o3*b - 2ex (?) (contains "2ike" as verf) o3/2x3o5/2o3*b - (contains "2ike") o3/2o3x5/2o3*b - sidtaxhi ``` ```x3o3o5/3o3/2*b - 2ex (?) (contains "2ike" as verf) o3x3o5/3o3/2*b - (contains "2ike") o3o3x5/3o3/2*b - sidtaxhi o3o3o5/3x3/2*b - sidtaxhi ``` otherWythoffians ```x3x3o5/2o3*b - (contains "2ike") x3o3x5/2o3*b - stut phiddix o3x3x5/2o3*b - wavhiddix o3o3x5/2x3*b - [Grünbaumian] x3x3x5/2o3*b - sphiddix x3o3x5/2x3*b - [Grünbaumian] o3x3x5/2x3*b - [Grünbaumian] x3x3x5/2x3*b - [Grünbaumian] ``` ```x3/2x3o5/2o3*b - [Grünbaumian] x3/2o3x5/2o3*b - (contains "2thah") o3/2x3x5/2o3*b - wavhiddix o3/2o3x5/2x3*b - [Grünbaumian] x3/2x3x5/2o3*b - [Grünbaumian] x3/2o3x5/2x3*b - [Grünbaumian] o3/2x3x5/2x3*b - [Grünbaumian] x3/2x3x5/2x3*b - [Grünbaumian] ``` ```x3x3o5/3o3/2*b - (contains "2ike") x3o3x5/3o3/2*b - stut phiddix x3o3o5/3x3/2*b - (contains "2thah") o3x3x5/3o3/2*b - wavhiddix o3x3o5/3x3/2*b - [Grünbaumian] o3o3x5/3x3/2*b - (contains "2geihid") x3x3x5/3o3/2*b - sphiddix x3x3o5/3x3/2*b - [Grünbaumian] x3o3x5/3x3/2*b - o3x3x5/3x3/2*b - [Grünbaumian] x3x3x5/3x3/2*b - [Grünbaumian] ``` (partial)snubs andholosnubs ```... ``` ```... ``` ```... ``` o3o3/2o5/2o3/2*b (µ=1202) o3/2o3/2o5/2o3/2*b (µ=1438) o3/2o3o5/3o3/2*b (µ=1562) quasiregulars ```x3o3/2o5/2o3/2*b - 2ex (?) (contains "2ike" as verf) o3x3/2o5/2o3/2*b - (contains "2ike") o3o3/2x5/2o3/2*b - sidtaxhi ``` ```x3/2o3/2o5/2o3/2*b - 2ex (?) (contains "2ike" as verf) o3/2x3/2o5/2o3/2*b - (contains "2ike") o3/2o3/2x5/2o3/2*b - sidtaxhi ``` ```x3/2o3o5/3o3/2*b - 2ex (?) (contains "2ike" as verf) o3/2x3o5/3o3/2*b - (contains "2ike") o3/2o3x5/3o3/2*b - sidtaxhi o3/2o3o5/3x3/2*b - sidtaxhi ``` otherWythoffians ```x3x3/2o5/2o3/2*b - (contains "2ike") x3o3/2x5/2o3/2*b - (contains "2thah") o3x3/2x5/2o3/2*b - [Grünbaumian] o3o3/2x5/2x3/2*b - [Grünbaumian] x3x3/2x5/2o3/2*b - [Grünbaumian] x3o3/2x5/2x3/2*b - [Grünbaumian] o3x3/2x5/2x3/2*b - [Grünbaumian] x3x3/2x5/2x3/2*b - [Grünbaumian] ``` ```x3/2x3/2o5/2o3/2*b - [Grünbaumian] x3/2o3/2x5/2o3/2*b - stut phiddix o3/2x3/2x5/2o3/2*b - [Grünbaumian] o3/2o3/2x5/2x3/2*b - [Grünbaumian] x3/2x3/2x5/2o3/2*b - [Grünbaumian] x3/2o3/2x5/2x3/2*b - [Grünbaumian] o3/2x3/2x5/2x3/2*b - [Grünbaumian] x3/2x3/2x5/2x3/2*b - [Grünbaumian] ``` ```x3/2x3o5/3o3/2*b - [Grünbaumian] x3/2o3x5/3o3/2*b - (contains "2thah") x3/2o3o5/3x3/2*b - stut phiddix o3/2x3x5/3o3/2*b - wavhiddix o3/2x3o5/3x3/2*b - [Grünbaumian] o3/2o3x5/3x3/2*b - (contains "2geihid") x3/2x3x5/3o3/2*b - [Grünbaumian] x3/2x3o5/3x3/2*b - [Grünbaumian] x3/2o3x5/3x3/2*b - o3/2x3x5/3x3/2*b - [Grünbaumian] x3/2x3x5/3x3/2*b - [Grünbaumian] ``` (partial)snubs andholosnubs ```... ``` ```... ``` ```... ```

### Hecatonicosachoral ("hyic") Symmetries – type o3o3/2o5o5*b   (up)

 o3o3/2o5o5*b (µ=3) o3o3o5/4o5*b (µ=117) o3/2o3/2o5o5*b (µ=237) o3o3o5o5/4*b (µ=483) quasiregulars ```x3o3/2o5o5*b - ex+fix (?) (contains cid as verf) o3x3/2o5o5*b - (contains cid) o3o3/2x5o5*b - (contains cid) o3o3/2o5x5*b - (contains "2doe") ``` ```x3o3o5/4o5*b - ex+fix (?) (contains cid as verf) o3x3o5/4o5*b - (contains cid) o3o3x5/4o5*b - (contains cid) o3o3o5/4x5*b - (contains "2doe") ``` ```x3/2o3/2o5o5*b - ex+fix (?) (contains cid as verf) o3/2x3/2o5o5*b - (contains cid) o3/2o3/2x5o5*b - (contains cid) o3/2o3/2o5x5*b - (contains "2doe") ``` ```x3o3o5o5/4*b - ex+fix (?) (contains cid as verf) o3x3o5o5/4*b - (contains cid) o3o3x5o5/4*b - (contains cid) o3o3o5x5/4*b - (contains "2doe") ``` otherWythoffians ```x3x3/2o5o5*b - (contains cid) x3o3/2x5o5*b - (contains cid) x3o3/2o5x5*b - (contains "2doe") o3x3/2x5o5*b - [Grünbaumian] o3x3/2o5x5*b - srawvixady o3o3/2x5x5*b - sixhihy x3x3/2x5o5*b - [Grünbaumian] x3x3/2o5x5*b - spixady x3o3/2x5x5*b - o3x3/2x5x5*b - [Grünbaumian] x3x3/2x5x5*b - [Grünbaumian] ``` ```x3x3o5/4o5*b - (contains cid) x3o3x5/4o5*b - (contains cid) x3o3o5/4x5*b - (contains "2doe") o3x3x5/4o5*b - (contains "2gidhei") o3x3o5/4x5*b - srawvixady o3o3x5/4x5*b - [Grünbaumian] x3x3x5/4o5*b - (contains "2gidhei") x3x3o5/4x5*b - spixady x3o3x5/4x5*b - [Grünbaumian] o3x3x5/4x5*b - [Grünbaumian] x3x3x5/4x5*b - [Grünbaumian] ``` ```x3/2x3/2o5o5*b - [Grünbaumian] x3/2o3/2x5o5*b - (contains cid) x3/2o3/2o5x5*b - (contains "2doe") o3/2x3/2x5o5*b - [Grünbaumian] o3/2x3/2o5x5*b - srawvixady o3/2o3/2x5x5*b - sixhihy x3/2x3/2x5o5*b - [Grünbaumian] x3/2x3/2o5x5*b - [Grünbaumian] x3/2o3/2x5x5*b - o3/2x3/2x5x5*b - [Grünbaumian] x3/2x3/2x5x5*b - [Grünbaumian] ``` ```x3x3o5o5/4*b - (contains cid) x3o3x5o5/4*b - (contains cid) x3o3o5x5/4*b - (contains "2doe") o3x3x5o5/4*b - (contains "2gidhei") o3x3o5x5/4*b - [Grünbaumian] o3o3x5x5/4*b - sixhihy x3x3x5o5/4*b - (contains "2gidhei") x3x3o5x5/4*b - [Grünbaumian] x3o3x5x5/4*b - o3x3x5x5/4*b - [Grünbaumian] x3x3x5x5/4*b - [Grünbaumian] ``` (partial)snubs andholosnubs ```... ``` ```... ``` ```... ``` ```... ``` o3/2o3o5o5/4*b (µ=717) o3/2o3o5/4o5*b (µ=1083) o3o3/2o5/4o5/4*b (µ=1797) o3/2o3/2o5/4o5/4*b (µ=2763) quasiregulars ```x3/2o3o5o5/4*b - ex+fix (?) (contains cid as verf) o3/2x3o5o5/4*b - (contains cid) o3/2o3x5o5/4*b - (contains cid) o3/2o3o5x5/4*b - (contains "2doe") ``` ```x3/2o3o5/4o5*b - ex+fix (?) (contains cid as verf) o3/2x3o5/4o5*b - (contains cid) o3/2o3x5/4o5*b - (contains cid) o3/2o3o5/4x5*b - (contains "2doe") ``` ```x3o3/2o5/4o5/4*b - ex+fix (?) (contains cid as verf) o3x3/2o5/4o5/4*b - (contains cid) o3o3/2x5/4o5/4*b - (contains cid) o3o3/2o5/4x5/4*b - (contains "2doe") ``` ```x3/2o3/2o5/4o5/4*b - ex+fix (?) (contains cid as verf) o3/2x3/2o5/4o5/4*b - (contains cid) o3/2o3/2x5/4o5/4*b - (contains cid) o3/2o3/2o5/4x5/4*b - (contains "2doe") ``` otherWythoffians ```x3/2x3o5o5/4*b - [Grünbaumian] x3/2o3x5o5/4*b - (contains cid) x3/2o3o5x5/4*b - (contains "2doe") o3/2x3x5o5/4*b - (contains "2gidhei") o3/2x3o5x5/4*b - [Grünbaumian] o3/2o3x5x5/4*b - sixhihy x3/2x3x5o5/4*b - [Grünbaumian] x3/2x3o5x5/4*b - [Grünbaumian] x3/2o3x5x5/4*b - o3/2x3x5x5/4*b - [Grünbaumian] x3/2x3x5x5/4*b - [Grünbaumian] ``` ```x3/2x3o5/4o5*b - [Grünbaumian] x3/2o3x5/4o5*b - (contains cid) x3/2o3o5/4x5*b - (contains "2doe") o3/2x3x5/4o5*b - (contains "2gidhei") o3/2x3o5/4x5*b - srawvixady o3/2o3x5/4x5*b - [Grünbaumian] x3/2x3x5/4o5*b - [Grünbaumian] x3/2x3o5/4x5*b - [Grünbaumian] x3/2o3x5/4x5*b - [Grünbaumian] o3/2x3x5/4x5*b - [Grünbaumian] x3/2x3x5/4x5*b - [Grünbaumian] ``` ```x3x3/2o5/4o5/4*b - (contains cid) x3o3/2x5/4o5/4*b - (contains cid) x3o3/2o5/4x5/4*b - (contains "2doe") o3x3/2x5/4o5/4*b - [Grünbaumian] o3x3/2o5/4x5/4*b - [Grünbaumian] o3o3/2x5/4x5/4*b - [Grünbaumian] x3x3/2x5/4o5/4*b - [Grünbaumian] x3x3/2o5/4x5/4*b - [Grünbaumian] x3o3/2x5/4x5/4*b - [Grünbaumian] o3x3/2x5/4x5/4*b - [Grünbaumian] x3x3/2x5/4x5/4*b - [Grünbaumian] ``` ```x3/2x3/2o5/4o5/4*b - [Grünbaumian] x3/2o3/2x5/4o5/4*b - (contains cid) x3/2o3/2o5/4x5/4*b - (contains "2doe") o3/2x3/2x5/4o5/4*b - [Grünbaumian] o3/2x3/2o5/4x5/4*b - [Grünbaumian] o3/2o3/2x5/4x5/4*b - [Grünbaumian] x3/2x3/2x5/4o5/4*b - [Grünbaumian] x3/2x3/2o5/4x5/4*b - [Grünbaumian] x3/2o3/2x5/4x5/4*b - [Grünbaumian] o3/2x3/2x5/4x5/4*b - [Grünbaumian] x3/2x3/2x5/4x5/4*b - [Grünbaumian] ``` (partial)snubs andholosnubs ```... ``` ```... ``` ```... ``` ```... ```

### Hecatonicosachoral ("hyic") Symmetries – type o3o3o5/3o5/2*b   (up)

 o3o3o5/3o5/2*b (µ=267) o3o3o5/2o5/3*b (µ=333) o3o3/2o5/2o5/2*b (µ=573) o3/2o3o5/2o5/3*b (µ=867) quasiregulars ```x3o3o5/3o5/2*b - gax+gofix (?) (contains gacid as verf) o3x3o5/3o5/2*b - (contains gacid) o3o3x5/3o5/2*b - (contains gacid) o3o3o5/3x5/2*b - (contains "2gissid") ``` ```x3o3o5/2o5/3*b - gax+gofix (?) (contains gacid as verf) o3x3o5/2o5/3*b - (contains gacid) o3o3x5/2o5/3*b - (contains gacid) o3o3o5/2x5/3*b - (contains "2gissid") ``` ```x3o3/2o5/2o5/2*b - gax+gofix (?) (contains gacid as verf) o3x3/2o5/2o5/2*b - (contains gacid) o3o3/2x5/2o5/2*b - (contains gacid) o3o3/2o5/2x5/2*b - (contains "2gissid") ``` ```x3/2o3o5/2o5/3*b - gax+gofix (?) (contains gacid as verf) o3/2x3o5/2o5/3*b - (contains gacid) o3/2o3x5/2o5/3*b - (contains gacid) o3/2o3o5/2x5/3*b - (contains "2gissid") ``` otherWythoffians ```x3x3o5/3o5/2*b - (contains gacid) x3o3x5/3o5/2*b - (contains gacid) x3o3o5/3x5/2*b - (contains "2gissid") o3x3x5/3o5/2*b - (contains "2sidhei") o3x3o5/3x5/2*b - [Grünbaumian] o3o3x5/3x5/2*b - gixhihy x3x3x5/3o5/2*b - (contains "2sidhei") x3x3o5/3x5/2*b - [Grünbaumian] x3o3x5/3x5/2*b - o3x3x5/3x5/2*b - [Grünbaumian] x3x3x5/3x5/2*b - [Grünbaumian] ``` ```x3x3o5/2o5/3*b - (contains gacid) x3o3x5/2o5/3*b - (contains gacid) x3o3o5/2x5/3*b - (contains "2gissid") o3x3x5/2o5/3*b - (contains "2sidhei") o3x3o5/2x5/3*b - gwavixady o3o3x5/2x5/3*b - [Grünbaumian] x3x3x5/2o5/3*b - (contains "2sidhei") x3x3o5/2x5/3*b - gippixady x3o3x5/2x5/3*b - [Grünbaumian] o3x3x5/2x5/3*b - [Grünbaumian] x3x3x5/2x5/3*b - [Grünbaumian] ``` ```x3x3/2o5/2o5/2*b - (contains gacid) x3o3/2x5/2o5/2*b - (contains gacid) x3o3/2o5/2x5/2*b - (contains "2gissid") o3x3/2x5/2o5/2*b - [Grünbaumian] o3x3/2o5/2x5/2*b - [Grünbaumian] o3o3/2x5/2x5/2*b - [Grünbaumian] x3x3/2x5/2o5/2*b - [Grünbaumian] x3x3/2o5/2x5/2*b - [Grünbaumian] x3o3/2x5/2x5/2*b - [Grünbaumian] o3x3/2x5/2x5/2*b - [Grünbaumian] x3x3/2x5/2x5/2*b - [Grünbaumian] ``` ```x3/2x3o5/2o5/3*b - [Grünbaumian] x3/2o3x5/2o5/3*b - (contains gacid) x3/2o3o5/2x5/3*b - (contains "2gissid") o3/2x3x5/2o5/3*b - (contains "2sidhei") o3/2x3o5/2x5/3*b - gwavixady o3/2o3x5/2x5/3*b - [Grünbaumian] x3/2x3x5/2o5/3*b - [Grünbaumian] x3/2x3o5/2x5/3*b - [Grünbaumian] x3/2o3x5/2x5/3*b - [Grünbaumian] o3/2x3x5/2x5/3*b - [Grünbaumian] x3/2x3x5/2x5/3*b - [Grünbaumian] ``` (partial)snubs andholosnubs ```... ``` ```... ``` ```... ``` ```... ``` o3/2o3o5/3o5/2*b (µ=933) o3/2o3/2o5/2o5/2*b (µ=1107) o3o3/2o5/3o5/3*b (µ=1227) o3/2o3/2o5/3o5/3*b (µ=1893) quasiregulars ```x3/2o3o5/3o5/2*b - gax+gofix (?) (contains gacid as verf) o3/2x3o5/3o5/2*b - (contains gacid) o3/2o3x5/3o5/2*b - (contains gacid) o3/2o3o5/3x5/2*b - (contains "2gissid") ``` ```x3/2o3/2o5/2o5/2*b - gax+gofix (?) (contains gacid as verf) o3/2x3/2o5/2o5/2*b - (contains gacid) o3/2o3/2x5/2o5/2*b - (contains gacid) o3/2o3/2o5/2x5/2*b - (contains "2gissid") ``` ```x3o3/2o5/3o5/3*b - gax+gofix (?) (contains gacid as verf) o3x3/2o5/3o5/3*b - (contains gacid) o3o3/2x5/3o5/3*b - (contains gacid) o3o3/2o5/3x5/3*b - (contains "2gissid") ``` ```x3/2o3/2o5/3o5/3*b - gax+gofix (?) (contains gacid as verf) o3/2x3/2o5/3o5/3*b - (contains gacid) o3/2o3/2x5/3o5/3*b - (contains gacid) o3/2o3/2o5/3x5/3*b - (contains "2gissid") ``` otherWythoffians ```x3/2x3o5/3o5/2*b - [Grünbaumian] x3/2o3x5/3o5/2*b - (contains gacid) x3/2o3o5/3x5/2*b - (contains "2gissid") o3/2x3x5/3o5/2*b - (contains "2sidhei") o3/2x3o5/3x5/2*b - [Grünbaumian] o3/2o3x5/3x5/2*b - gixhihy x3/2x3x5/3o5/2*b - [Grünbaumian] x3/2x3o5/3x5/2*b - [Grünbaumian] x3/2o3x5/3x5/2*b - o3/2x3x5/3x5/2*b - [Grünbaumian] x3/2x3x5/3x5/2*b - [Grünbaumian] ``` ```x3/2x3/2o5/2o5/2*b - [Grünbaumian] x3/2o3/2x5/2o5/2*b - (contains gacid) x3/2o3/2o5/2x5/2*b - (contains "2gissid") o3/2x3/2x5/2o5/2*b - [Grünbaumian] o3/2x3/2o5/2x5/2*b - [Grünbaumian] o3/2o3/2x5/2x5/2*b - [Grünbaumian] x3/2x3/2x5/2o5/2*b - [Grünbaumian] x3/2x3/2o5/2x5/2*b - [Grünbaumian] x3/2o3/2x5/2x5/2*b - [Grünbaumian] o3/2x3/2x5/2x5/2*b - [Grünbaumian] x3/2x3/2x5/2x5/2*b - [Grünbaumian] ``` ```x3x3/2o5/3o5/3*b - (contains gacid) x3o3/2x5/3o5/3*b - (contains gacid) x3o3/2o5/3x5/3*b - (contains "2gissid") o3x3/2x5/3o5/3*b - [Grünbaumian] o3x3/2o5/3x5/3*b - gwavixady o3o3/2x5/3x5/3*b - gixhihy x3x3/2x5/3o5/3*b - [Grünbaumian] x3x3/2o5/3x5/3*b - gippixady x3o3/2x5/3x5/3*b - o3x3/2x5/3x5/3*b - [Grünbaumian] x3x3/2x5/3x5/3*b - [Grünbaumian] ``` ```x3/2x3/2o5/3o5/3*b - [Grünbaumian] x3/2o3/2x5/3o5/3*b - (contains gacid) x3/2o3/2o5/3x5/3*b - (contains "2gissid") o3/2x3/2x5/3o5/3*b - [Grünbaumian] o3/2x3/2o5/3x5/3*b - gwavixady o3/2o3/2x5/3x5/3*b - gixhihy x3/2x3/2x5/3o5/3*b - [Grünbaumian] x3/2x3/2o5/3x5/3*b - [Grünbaumian] x3/2o3/2x5/3x5/3*b - o3/2x3/2x5/3x5/3*b - [Grünbaumian] x3/2x3/2x5/3x5/3*b - [Grünbaumian] ``` (partial)snubs andholosnubs ```... ``` ```... ``` ```... ``` ```... ```

### Hecatonicosachoral ("hyic") Symmetries – type o3o3o5o5/3*b   (up)

 o3o3o5o5/3*b (µ=115) o3o3/2o5o5/2*b (µ=355) o3/2o3o5o5/3*b (µ=365) o3o3o5/4o5/2*b (µ=485) quasiregulars ```x3o3o5o5/3*b - gax+gofix (?) (contains gacid as verf) o3x3o5o5/3*b - (contains gacid) o3o3x5o5/3*b - (contains cid) o3o3o5x5/3*b - gadatady ``` ```x3o3/2o5o5/2*b - gax+gofix (?) (contains gacid as verf) o3x3/2o5o5/2*b - (contains gacid) o3o3/2x5o5/2*b - (contains cid) o3o3/2o5x5/2*b - gadatady ``` ```x3/2o3o5o5/3*b - gax+gofix (?) (contains gacid as verf) o3/2x3o5o5/3*b - (contains gacid) o3/2o3x5o5/3*b - (contains cid) o3/2o3o5x5/3*b - gadatady ``` ```x3o3o5/4o5/2*b - gax+gofix (?) (contains gacid as verf) o3x3o5/4o5/2*b - (contains gacid) o3o3x5/4o5/2*b - (contains cid) o3o3o5/4x5/2*b - gadatady ``` otherWythoffians ```x3x3o5o5/3*b - (contains gacid) x3o3x5o5/3*b - (contains cid) x3o3o5x5/3*b - getit pixady o3x3x5o5/3*b - grawv hixhi o3x3o5x5/3*b - wavdatixady o3o3x5x5/3*b - sidthixhi x3x3x5o5/3*b - giphihix x3x3o5x5/3*b - gixipady x3o3x5x5/3*b - gikkiv datapixady o3x3x5x5/3*b - hixquathix x3x3x5x5/3*b - hixquitphix ``` ```x3x3/2o5o5/2*b - (contains gacid) x3o3/2x5o5/2*b - (contains cid) x3o3/2o5x5/2*b - (contains sicdatrid) o3x3/2x5o5/2*b - [Grünbaumian] o3x3/2o5x5/2*b - [Grünbaumian] o3o3/2x5x5/2*b - sidthixhi x3x3/2x5o5/2*b - [Grünbaumian] x3x3/2o5x5/2*b - [Grünbaumian] x3o3/2x5x5/2*b - o3x3/2x5x5/2*b - [Grünbaumian] x3x3/2x5x5/2*b - [Grünbaumian] ``` ```x3/2x3o5o5/3*b - [Grünbaumian] x3/2o3x5o5/3*b - (contains cid) x3/2o3o5x5/3*b - (contains sicdatrid) o3/2x3x5o5/3*b - grawv hixhi o3/2x3o5x5/3*b - wavdatixady o3/2o3x5x5/3*b - sidthixhi x3/2x3x5o5/3*b - [Grünbaumian] x3/2x3o5x5/3*b - [Grünbaumian] x3/2o3x5x5/3*b - o3/2x3x5x5/3*b - hixquathix x3/2x3x5x5/3*b - [Grünbaumian] ``` ```x3x3o5/4o5/2*b - (contains gacid) x3o3x5/4o5/2*b - (contains cid) x3o3o5/4x5/2*b - (contains sicdatrid) o3x3x5/4o5/2*b - grawv hixhi o3x3o5/4x5/2*b - [Grünbaumian] o3o3x5/4x5/2*b - [Grünbaumian] x3x3x5/4o5/2*b - giphihix x3x3o5/4x5/2*b - [Grünbaumian] x3o3x5/4x5/2*b - [Grünbaumian] o3x3x5/4x5/2*b - [Grünbaumian] x3x3x5/4x5/2*b - [Grünbaumian] ``` (partial)snubs andholosnubs ```... ``` ```... ``` ```... ``` ```... ``` o3/2o3/2o5o5/2*b (µ=605) o3/2o3o5/4o5/2*b (µ=1435) o3o3/2o5/4o5/3*b (µ=1445) o3/2o3/2o5/4o5/3*b (µ=2395) quasiregulars ```x3/2o3/2o5o5/2*b - gax+gofix (?) (contains gacid as verf) o3/2x3/2o5o5/2*b - (contains gacid) o3/2o3/2x5o5/2*b - (contains cid) o3/2o3/2o5x5/2*b - gadatady ``` ```x3/2o3o5/4o5/2*b - gax+gofix (?) (contains gacid as verf) o3/2x3o5/4o5/2*b - (contains gacid) o3/2o3x5/4o5/2*b - (contains cid) o3/2o3o5/4x5/2*b - gadatady ``` ```x3o3/2o5/4o5/3*b - gax+gofix (?) (contains gacid as verf) o3x3/2o5/4o5/3*b - (contains gacid) o3o3/2x5/4o5/3*b - (contains cid) o3o3/2o5/4x5/3*b - gadatady ``` ```x3/2o3/2o5/4o5/3*b - gax+gofix (?) (contains gacid as verf) o3/2x3/2o5/4o5/3*b - (contains gacid) o3/2o3/2x5/4o5/3*b - (contains cid) o3/2o3/2o5/4x5/3*b - gadatady ``` otherWythoffians ```x3/2x3/2o5o5/2*b - [Grünbaumian] x3/2o3/2x5o5/2*b - (contains cid) x3/2o3/2o5x5/2*b - getit pixady o3/2x3/2x5o5/2*b - [Grünbaumian] o3/2x3/2o5x5/2*b - [Grünbaumian] o3/2o3/2x5x5/2*b - sidthixhi x3/2x3/2x5o5/2*b - [Grünbaumian] x3/2x3/2o5x5/2*b - [Grünbaumian] x3/2o3/2x5x5/2*b - gikkiv datapixady o3/2x3/2x5x5/2*b - [Grünbaumian] x3/2x3/2x5x5/2*b - [Grünbaumian] ``` ```x3/2x3o5/4o5/2*b - [Grünbaumian] x3/2o3x5/4o5/2*b - (contains cid) x3/2o3o5/4x5/2*b - getit pixady o3/2x3x5/4o5/2*b - grawv hixhi o3/2x3o5/4x5/2*b - [Grünbaumian] o3/2o3x5/4x5/2*b - [Grünbaumian] x3/2x3x5/4o5/2*b - [Grünbaumian] x3/2x3o5/4x5/2*b - [Grünbaumian] x3/2o3x5/4x5/2*b - [Grünbaumian] o3/2x3x5/4x5/2*b - [Grünbaumian] x3/2x3x5/4x5/2*b - [Grünbaumian] ``` ```x3x3/2o5/4o5/3*b - (contains gacid) x3o3/2x5/4o5/3*b - (contains cid) x3o3/2o5/4x5/3*b - getit pixady o3x3/2x5/4o5/3*b - [Grünbaumian] o3x3/2o5/4x5/3*b - wavdatixady o3o3/2x5/4x5/3*b - [Grünbaumian] x3x3/2x5/4o5/3*b - [Grünbaumian] x3x3/2o5/4x5/3*b - gixipady x3o3/2x5/4x5/3*b - [Grünbaumian] o3x3/2x5/4x5/3*b - [Grünbaumian] x3x3/2x5/4x5/3*b - [Grünbaumian] ``` ```x3/2x3/2o5/4o5/3*b - [Grünbaumian] x3/2o3/2x5/4o5/3*b - (contains cid) x3/2o3/2o5/4x5/3*b - (contains sicdatrid) o3/2x3/2x5/4o5/3*b - [Grünbaumian] o3/2x3/2o5/4x5/3*b - wavdatixady o3/2o3/2x5/4x5/3*b - [Grünbaumian] x3/2x3/2x5/4o5/3*b - [Grünbaumian] x3/2x3/2o5/4x5/3*b - [Grünbaumian] x3/2o3/2x5/4x5/3*b - [Grünbaumian] o3/2x3/2x5/4x5/3*b - [Grünbaumian] x3/2x3/2x5/4x5/3*b - [Grünbaumian] ``` (partial)snubs andholosnubs ```... ``` ```... ``` ```... ``` ```... ```

### Hecatonicosachoral ("hyic") Symmetries – type o3o3o5/3o5*b   (up)

 o3o3o5/3o5*b (µ=5) o3o3/2o5/2o5*b (µ=115) o3/2o3o5/3o5*b (µ=475) o3o3o5/2o5/4*b (µ=595) quasiregulars ```x3o3o5/3o5*b - ex+fix (?) (contains cid as verf) o3x3o5/3o5*b - (contains cid) o3o3x5/3o5*b - (contains gacid) o3o3o5/3x5*b - siddatady ``` ```x3o3/2o5/2o5*b - ex+fix (?) (contains cid as verf) o3x3/2o5/2o5*b - (contains cid) o3o3/2x5/2o5*b - (contains gacid) o3o3/2o5/2x5*b - siddatady ``` ```x3/2o3o5/3o5*b - ex+fix (?) (contains cid as verf) o3/2x3o5/3o5*b - (contains cid) o3/2o3x5/3o5*b - (contains gacid) o3/2o3o5/3x5*b - siddatady ``` ```x3o3o5/2o5/4*b - ex+fix (?) (contains cid as verf) o3x3o5/2o5/4*b - (contains cid) o3o3x5/2o5/4*b - (contains gacid) o3o3o5/2x5/4*b - siddatady ``` otherWythoffians ```x3x3o5/3o5*b - (contains cid) x3o3x5/3o5*b - (contains gacid) x3o3o5/3x5*b - stut pixady o3x3x5/3o5*b - mrawv hixhi o3x3o5/3x5*b - rawvid tixady o3o3x5/3x5*b - gidthixhi x3x3x5/3o5*b - sphihix x3x3o5/3x5*b - sixipady x3o3x5/3x5*b - skiv datapixady o3x3x5/3x5*b - hixthix x3x3x5/3x5*b - hixtaphix ``` ```x3x3/2o5/2o5*b - (contains cid) x3o3/2x5/2o5*b - (contains gacid) x3o3/2o5/2x5*b - stut pixady o3x3/2x5/2o5*b - [Grünbaumian] o3x3/2o5/2x5*b - rawvid tixady o3o3/2x5/2x5*b - [Grünbaumian] x3x3/2x5/2o5*b - [Grünbaumian] x3x3/2o5/2x5*b - sixipady x3o3/2x5/2x5*b - [Grünbaumian] o3x3/2x5/2x5*b - [Grünbaumian] x3x3/2x5/2x5*b - [Grünbaumian] ``` ```x3/2x3o5/3o5*b - [Grünbaumian] x3/2o3x5/3o5*b - (contains gacid) x3/2o3o5/3x5*b - (contains gicdatrid) o3/2x3x5/3o5*b - mrawv hixhi o3/2x3o5/3x5*b - rawvid tixady o3/2o3x5/3x5*b - gidthixhi x3/2x3x5/3o5*b - [Grünbaumian] x3/2x3o5/3x5*b - [Grünbaumian] x3/2o3x5/3x5*b - o3/2x3x5/3x5*b - hixthix x3/2x3x5/3x5*b - [Grünbaumian] ``` ```x3x3o5/2o5/4*b - (contains cid) x3o3x5/2o5/4*b - (contains gacid) x3o3o5/2x5/4*b - (contains gicdatrid) o3x3x5/2o5/4*b - mrawv hixhi o3x3o5/2x5/4*b - [Grünbaumian] o3o3x5/2x5/4*b - [Grünbaumian] x3x3x5/2o5/4*b - sphihix x3x3o5/2x5/4*b - [Grünbaumian] x3o3x5/2x5/4*b - [Grünbaumian] o3x3x5/2x5/4*b - [Grünbaumian] x3x3x5/2x5/4*b - [Grünbaumian] ``` (partial)snubs andholosnubs ```... ``` ```... ``` ```... ``` ```... ``` o3/2o3/2o5/2o5*b (µ=845) o3/2o3o5/2o5/4*b (µ=1325) o3o3/2o5/3o5/4*b (µ=1685) o3/2o3/2o5/3o5/4*b (µ=2155) quasiregulars ```x3/2o3/2o5/2o5*b - ex+fix (?) (contains cid as verf) o3/2x3/2o5/2o5*b - (contains cid) o3/2o3/2x5/2o5*b - (contains gacid) o3/2o3/2o5/2x5*b - siddatady ``` ```x3/2o3o5/2o5/4*b - ex+fix (?) (contains cid as verf) o3/2x3o5/2o5/4*b - (contains cid) o3/2o3x5/2o5/4*b - (contains gacid) o3/2o3o5/2x5/4*b - siddatady ``` ```x3o3/2o5/3o5/4*b - ex+fix (?) (contains cid as verf) o3x3/2o5/3o5/4*b - (contains cid) o3o3/2x5/3o5/4*b - (contains gacid) o3o3/2o5/3x5/4*b - siddatady ``` ```x3/2o3/2o5/3o5/4*b - ex+fix (?) (contains cid as verf) o3/2x3/2o5/3o5/4*b - (contains cid) o3/2o3/2x5/3o5/4*b - (contains gacid) o3/2o3/2o5/3x5/4*b - siddatady ``` otherWythoffians ```x3/2x3/2o5/2o5*b - [Grünbaumian] x3/2o3/2x5/2o5*b - (contains gacid) x3/2o3/2o5/2x5*b - (contains gicdatrid) o3/2x3/2x5/2o5*b - [Grünbaumian] o3/2x3/2o5/2x5*b - rawvid tixady o3/2o3/2x5/2x5*b - [Grünbaumian] x3/2x3/2x5/2o5*b - [Grünbaumian] x3/2x3/2o5/2x5*b - [Grünbaumian] x3/2o3/2x5/2x5*b - [Grünbaumian] o3/2x3/2x5/2x5*b - [Grünbaumian] x3/2x3/2x5/2x5*b - [Grünbaumian] ``` ```x3/2x3o5/2o5/4*b - [Grünbaumian] x3/2o3x5/2o5/4*b - (contains gacid) x3/2o3o5/2x5/4*b - stut pixady o3/2x3x5/2o5/4*b - mrawv hixhi o3/2x3o5/2x5/4*b - [Grünbaumian] o3/2o3x5/2x5/4*b - [Grünbaumian] x3/2x3x5/2o5/4*b - [Grünbaumian] x3/2x3o5/2x5/4*b - [Grünbaumian] x3/2o3x5/2x5/4*b - [Grünbaumian] o3/2x3x5/2x5/4*b - [Grünbaumian] x3/2x3x5/2x5/4*b - [Grünbaumian] ``` ```x3x3/2o5/3o5/4*b - (contains cid) x3o3/2x5/3o5/4*b - (contains gacid) x3o3/2o5/3x5/4*b - (contains gicdatrid) o3x3/2x5/3o5/4*b - [Grünbaumian] o3x3/2o5/3x5/4*b - [Grünbaumian] o3o3/2x5/3x5/4*b - gidthixhi x3x3/2x5/3o5/4*b - [Grünbaumian] x3x3/2o5/3x5/4*b - [Grünbaumian] x3o3/2x5/3x5/4*b - o3x3/2x5/3x5/4*b - [Grünbaumian] x3x3/2x5/3x5/4*b - [Grünbaumian] ``` ```x3/2x3/2o5/3o5/4*b - [Grünbaumian] x3/2o3/2x5/3o5/4*b - (contains gacid) x3/2o3/2o5/3x5/4*b - stut pixady o3/2x3/2x5/3o5/4*b - [Grünbaumian] o3/2x3/2o5/3x5/4*b - [Grünbaumian] o3/2o3/2x5/3x5/4*b - gidthixhi x3/2x3/2x5/3o5/4*b - [Grünbaumian] x3/2x3/2o5/3x5/4*b - [Grünbaumian] x3/2o3/2x5/3x5/4*b - skiv datapixady o3/2x3/2x5/3x5/4*b - [Grünbaumian] x3/2x3/2x5/3x5/4*b - [Grünbaumian] ``` (partial)snubs andholosnubs ```... ``` ```... ``` ```... ``` ```... ```

### Hecatonicosachoral ("hyic") Symmetries – type o3o5o3o5/3*b   (up)

 o3o5o3o5/3*b (µ=30) o3o5o3/2o5/2*b (µ=90) o3/2o5o3o5/3*b (µ=450) o3o5/4o3o5/2*b (µ=750) quasiregulars ```x3o5o3o5/3*b - dittady o3x5o3o5/3*b - ridtidohi o3o5x3o5/3*b - (contains cid) o3o5o3x5/3*b - (contains gacid) ``` ```x3o5o3/2o5/2*b - dittady o3x5o3/2o5/2*b - ridtidohi o3o5x3/2o5/2*b - (contains cid) o3o5o3/2x5/2*b - (contains gacid) ``` ```x3/2o5o3o5/3*b - dittady o3/2x5o3o5/3*b - ridtidohi o3/2o5x3o5/3*b - (contains cid) o3/2o5o3x5/3*b - (contains gacid) ``` ```x3o5/4o3o5/2*b - dittady o3x5/4o3o5/2*b - ridtidohi o3o5/4x3o5/2*b - (contains cid) o3o5/4o3x5/2*b - (contains gacid) ``` otherWythoffians ```x3x5o3o5/3*b - tidtidohi x3o5x3o5/3*b - (contains cid) x3o5o3x5/3*b - (contains gacid) o3x5x3o5/3*b - srawv ditathi o3x5o3x5/3*b - gwav ditathi o3o5x3x5/3*b - tahi x3x5x3o5/3*b - sid tipathi x3x5o3x5/3*b - gid tipathi x3o5x3x5/3*b - o3x5x3x5/3*b - hihiquatady x3x5x3x5/3*b - dohitipady ``` ```x3x5o3/2o5/2*b - tidtidohi x3o5x3/2o5/2*b - (contains cid) x3o5o3/2x5/2*b - (contains gacid) o3x5x3/2o5/2*b - srawv ditathi o3x5o3/2x5/2*b - [Grünbaumian] o3o5x3/2x5/2*b - [Grünbaumian] x3x5x3/2o5/2*b - sid tipathi x3x5o3/2x5/2*b - [Grünbaumian] x3o5x3/2x5/2*b - [Grünbaumian] o3x5x3/2x5/2*b - [Grünbaumian] x3x5x3/2x5/2*b - [Grünbaumian] ``` ```x3/2x5o3o5/3*b - [Grünbaumian] x3/2o5x3o5/3*b - (contains cid) x3/2o5o3x5/3*b - (contains gacid) o3/2x5x3o5/3*b - srawv ditathi o3/2x5o3x5/3*b - gwav ditathi o3/2o5x3x5/3*b - tahi x3/2x5x3o5/3*b - [Grünbaumian] x3/2x5o3x5/3*b - [Grünbaumian] x3/2o5x3x5/3*b - o3/2x5x3x5/3*b - hihiquatady x3/2x5x3x5/3*b - [Grünbaumian] ``` ```x3x5/4o3o5/2*b - tidtidohi x3o5/4x3o5/2*b - (contains cid) x3o5/4o3x5/2*b - (contains gacid) o3x5/4x3o5/2*b - [Grünbaumian] o3x5/4o3x5/2*b - [Grünbaumian] o3o5/4x3x5/2*b - tahi x3x5/4x3o5/2*b - [Grünbaumian] x3x5/4o3x5/2*b - [Grünbaumian] x3o5/4x3x5/2*b - o3x5/4x3x5/2*b - [Grünbaumian] x3x5/4x3x5/2*b - [Grünbaumian] ``` (partial)snubs andholosnubs ```... ``` ```... ``` ```... ``` ```... ``` o3/2o5o3/2o5/2*b (µ=870) o3/2o5/4o3o5/2*b (µ=1170) o3o5/4o3/2o5/3*b (µ=1530) o3/2o5/4o3/2o5/3*b (µ=2310) quasiregulars ```x3/2o5o3/2o5/2*b - dittady o3/2x5o3/2o5/2*b - ridtidohi o3/2o5x3/2o5/2*b - (contains cid) o3/2o5o3/2x5/2*b - (contains gacid) ``` ```x3/2o5/4o3o5/2*b - dittady o3/2x5/4o3o5/2*b - ridtidohi o3/2o5/4x3o5/2*b - (contains cid) o3/2o5/4o3x5/2*b - (contains gacid) ``` ```x3o5/4o3/2o5/3*b - dittady o3x5/4o3/2o5/3*b - ridtidohi o3o5/4x3/2o5/3*b - (contains cid) o3o5/4o3/2x5/3*b - (contains gacid) ``` ```x3/2o5/4o3/2o5/3*b - dittady o3/2x5/4o3/2o5/3*b - ridtidohi o3/2o5/4x3/2o5/3*b - (contains cid) o3/2o5/4o3/2x5/3*b - (contains gacid) ``` otherWythoffians ```x3/2x5o3/2o5/2*b - [Grünbaumian] x3/2o5x3/2o5/2*b - (contains cid) x3/2o5o3/2x5/2*b - (contains gacid) o3/2x5x3/2o5/2*b - srawv ditathi o3/2x5o3/2x5/2*b - [Grünbaumian] o3/2o5x3/2x5/2*b - [Grünbaumian] x3/2x5x3/2o5/2*b - [Grünbaumian] x3/2x5o3/2x5/2*b - [Grünbaumian] x3/2o5x3/2x5/2*b - [Grünbaumian] o3/2x5x3/2x5/2*b - [Grünbaumian] x3/2x5x3/2x5/2*b - [Grünbaumian] ``` ```x3/2x5/4o3o5/2*b - [Grünbaumian] x3/2o5/4x3o5/2*b - (contains cid) x3/2o5/4o3x5/2*b - (contains gacid) o3/2x5/4x3o5/2*b - [Grünbaumian] o3/2x5/4o3x5/2*b - [Grünbaumian] o3/2o5/4x3x5/2*b - tahi x3/2x5/4x3o5/2*b - [Grünbaumian] x3/2x5/4o3x5/2*b - [Grünbaumian] x3/2o5/4x3x5/2*b - o3/2x5/4x3x5/2*b - [Grünbaumian] x3/2x5/4x3x5/2*b - [Grünbaumian] ``` ```x3x5/4o3/2o5/3*b - tidtidohi x3o5/4x3/2o5/3*b - (contains cid) x3o5/4o3/2x5/3*b - (contains gacid) o3x5/4x3/2o5/3*b - [Grünbaumian] o3x5/4o3/2x5/3*b - gwav ditathi o3o5/4x3/2x5/3*b - [Grünbaumian] x3x5/4x3/2o5/3*b - [Grünbaumian] x3x5/4o3/2x5/3*b - gid tipathi x3o5/4x3/2x5/3*b - [Grünbaumian] o3x5/4x3/2x5/3*b - [Grünbaumian] x3x5/4x3/2x5/3*b - [Grünbaumian] ``` ```x3/2x5/4o3/2o5/3*b - [Grünbaumian] x3/2o5/4x3/2o5/3*b - (contains cid) x3/2o5/4o3/2x5/3*b - (contains gacid) o3/2x5/4x3/2o5/3*b - [Grünbaumian] o3/2x5/4o3/2x5/3*b - gwav ditathi o3/2o5/4x3/2x5/3*b - [Grünbaumian] x3/2x5/4x3/2o5/3*b - [Grünbaumian] x3/2x5/4o3/2x5/3*b - [Grünbaumian] x3/2o5/4x3/2x5/3*b - [Grünbaumian] o3/2x5/4x3/2x5/3*b - [Grünbaumian] x3/2x5/4x3/2x5/3*b - [Grünbaumian] ``` (partial)snubs andholosnubs ```... ``` ```... ``` ```... ``` ```... ```

### Hecatonicosachoral ("hyic") Symmetries – type o3o5o5/4o5*b   (up)

 o3o5o5/4o5*b (µ=8) o3o5o5o5/4*b (µ=112) o3/2o5o5o5/4*b (µ=608) quasiregulars ```x3o5o5/4o5*b - 2fix (?) (contains "2gad" as verf) o3x5o5/4o5*b - (contains "2gad") o3o5x5/4o5*b - (contains "2gad") ``` ```x3o5o5o5/4*b - 2fix (?) (contains "2gad" as verf) o3x5o5o5/4*b - (contains "2gad") o3o5x5o5/4*b - (contains "2gad") o3o5o5x5/4*b - (contains "2gad") ``` ```x3/2o5o5o5/4*b - 2fix (?) (contains "2gad" as verf) o3/2x5o5o5/4*b - (contains "2gad") o3/2o5x5o5/4*b - (contains "2gad") o3/2o5o5x5/4*b - (contains "2gad") ``` otherWythoffians ```x3x5o5/4o5*b - (contains "2gad") x3o5x5/4o5*b - (contains "2gad") o3x5x5/4o5*b - (contains "2sidhid") o3o5x5/4x5*b - [Grünbaumian] x3x5x5/4o5*b - (contains "2sidhid") x3o5x5/4x5*b - [Grünbaumian] o3x5x5/4x5*b - [Grünbaumian] x3x5x5/4x5*b - [Grünbaumian] ``` ```x3x5o5o5/4*b - (contains "2gad") x3o5x5o5/4*b - (contains "2gad") x3o5o5x5/4*b - (contains "2gad") o3x5x5o5/4*b - (contains "2sidhid") o3x5o5x5/4*b - [Grünbaumian] o3o5x5x5/4*b - (contains "2sidhid") x3x5x5o5/4*b - (contains "2sidhid") x3x5o5x5/4*b - [Grünbaumian] x3o5x5x5/4*b - o3x5x5x5/4*b - [Grünbaumian] x3x5x5x5/4*b - [Grünbaumian] ``` ```x3/2x5o5o5/4*b - [Grünbaumian] x3/2o5x5o5/4*b - (contains "2gad") x3/2o5o5x5/4*b - (contains "2gad") o3/2x5x5o5/4*b - (contains "2sidhid") o3/2x5o5x5/4*b - [Grünbaumian] o3/2o5x5x5/4*b - (contains "2sidhid") x3/2x5x5o5/4*b - [Grünbaumian] x3/2x5o5x5/4*b - [Grünbaumian] x3/2o5x5x5/4*b - o3/2x5x5x5/4*b - [Grünbaumian] x3/2x5x5x5/4*b - [Grünbaumian] ``` (partial)snubs andholosnubs ```... ``` ```... ``` ```... ``` o3/2o5o5/4o5*b (µ=712) o3o5/4o5/4o5/4*b (µ=2168) o3/2o5/4o5/4o5/4*b (µ=2872) quasiregulars ```x3/2o5o5/4o5*b - 2fix (?) (contains "2gad" as verf) o3/2x5o5/4o5*b - (contains "2gad") o3/2o5x5/4o5*b - (contains "2gad") ``` ```x3o5/4o5/4o5/4*b - 2fix (?) (contains "2gad" as verf) o3x5/4o5/4o5/4*b - (contains "2gad") o3o5/4x5/4o5/4*b - (contains "2gad") ``` ```x3/2o5/4o5/4o5/4*b - 2fix (?) (contains "2gad" as verf) o3/2x5/4o5/4o5/4*b - (contains "2gad") o3/2o5/4x5/4o5/4*b - (contains "2gad") ``` otherWythoffians ```x3/2x5o5/4o5*b - [Grünbaumian] x3/2o5x5/4o5*b - (contains "2gad") o3/2x5x5/4o5*b - (contains "2sidhid") o3/2o5x5/4x5*b - [Grünbaumian] x3/2x5x5/4o5*b - [Grünbaumian] x3/2o5x5/4x5*b - [Grünbaumian] o3/2x5x5/4x5*b - [Grünbaumian] x3/2x5x5/4x5*b - [Grünbaumian] ``` ```x3x5/4o5/4o5/4*b - (contains "2gad") x3o5/4x5/4o5/4*b - (contains "2gad") o3x5/4x5/4o5/4*b - [Grünbaumian] o3o5/4x5/4x5/4*b - [Grünbaumian] x3x5/4x5/4o5/4*b - [Grünbaumian] x3o5/4x5/4x5/4*b - [Grünbaumian] o3x5/4x5/4x5/4*b - [Grünbaumian] x3x5/4x5/4x5/4*b - [Grünbaumian] ``` ```x3/2x5/4o5/4o5/4*b - [Grünbaumian] x3/2o5/4x5/4o5/4*b - (contains "2gad") o3/2x5/4x5/4o5/4*b - [Grünbaumian] o3/2o5/4x5/4x5/4*b - [Grünbaumian] x3/2x5/4x5/4o5/4*b - [Grünbaumian] x3/2o5/4x5/4x5/4*b - [Grünbaumian] o3/2x5/4x5/4x5/4*b - [Grünbaumian] x3/2x5/4x5/4x5/4*b - [Grünbaumian] ``` (partial)snubs andholosnubs ```... ``` ```... ``` ```... ```

### Hecatonicosachoral ("hyic") Symmetries – type o3o5/2o5/2o5/2*b   (up)

 o3o5/2o5/2o5/2*b (µ=152) o3/2o5/2o5/2o5/2*b (µ=568) o3o5/2o5/3o5/3*b (µ=688) quasiregulars ```x3o5/2o5/2o5/2*b - 2gofix (?) (contains "2sissid" as verf) o3x5/2o5/2o5/2*b - (contains "2sissid") o3o5/2x5/2o5/2*b - (contains "2sissid") ``` ```x3/2o5/2o5/2o5/2*b - 2gofix (?) (contains "2sissid" as verf) o3/2x5/2o5/2o5/2*b - (contains "2sissid") o3/2o5/2x5/2o5/2*b - (contains "2sissid") ``` ```x3o5/2o5/3o5/3*b - 2gofix (?) (contains "2sissid" as verf) o3x5/2o5/3o5/3*b - (contains "2sissid") o3o5/2x5/3o5/3*b - (contains "2sissid") o3o5/2o5/3x5/3*b - (contains "2sissid") ``` otherWythoffians ```x3x5/2o5/2o5/2*b - (contains "2sissid") x3o5/2x5/2o5/2*b - (contains "2sissid") o3x5/2x5/2o5/2*b - [Grünbaumian] o3o5/2x5/2x5/2*b - [Grünbaumian] x3x5/2x5/2o5/2*b - [Grünbaumian] x3o5/2x5/2x5/2*b - [Grünbaumian] o3x5/2x5/2x5/2*b - [Grünbaumian] x3x5/2x5/2x5/2*b - [Grünbaumian] ``` ```x3/2x5/2o5/2o5/2*b - [Grünbaumian] x3/2o5/2x5/2o5/2*b - (contains "2sissid") o3/2x5/2x5/2o5/2*b - [Grünbaumian] o3/2o5/2x5/2x5/2*b - [Grünbaumian] x3/2x5/2x5/2o5/2*b - [Grünbaumian] x3/2o5/2x5/2x5/2*b - [Grünbaumian] o3/2x5/2x5/2x5/2*b - [Grünbaumian] x3/2x5/2x5/2x5/2*b - [Grünbaumian] ``` ```x3x5/2o5/3o5/3*b - (contains "2sissid") x3o5/2x5/3o5/3*b - (contains "2sissid") x3o5/2o5/3x5/3*b - (contains "2sissid") o3x5/2x5/3o5/3*b - [Grünbaumian] o3x5/2o5/3x5/3*b - (contains "2gidhid") o3o5/2x5/3x5/3*b - (contains "2gidhid") x3x5/2x5/3o5/3*b - [Grünbaumian] x3x5/2o5/3x5/3*b - (contains "2gidhid") x3o5/2x5/3x5/3*b - o3x5/2x5/3x5/3*b - [Grünbaumian] x3x5/2x5/3x5/3*b - [Grünbaumian] ``` (partial)snubs andholosnubs ```... ``` ```... ``` ```... ``` o3o5/3o5/2o5/3*b (µ=872) o3/2o5/3o5/2o5/3*b (µ=1288) o3/2o5/2o5/3o5/3*b (µ=1472) quasiregulars ```x3o5/3o5/2o5/3*b - 2gofix (?) (contains "2sissid" as verf) o3x5/3o5/2o5/3*b - (contains "2sissid") o3o5/3x5/2o5/3*b - (contains "2sissid") ``` ```x3/2o5/3o5/2o5/3*b - 2gofix (?) (contains "2sissid" as verf) o3/2x5/3o5/2o5/3*b - (contains "2sissid") o3/2o5/3x5/2o5/3*b - (contains "2sissid") ``` ```x3/2o5/2o5/3o5/3*b - 2gofix (?) (contains "2sissid" as verf) o3/2x5/2o5/3o5/3*b - (contains "2sissid") o3/2o5/2x5/3o5/3*b - (contains "2sissid") o3/2o5/2o5/3x5/3*b - (contains "2sissid") ``` otherWythoffians ```x3x5/3o5/2o5/3*b - (contains "2sissid") x3o5/3x5/2o5/3*b - (contains "2sissid") o3x5/3x5/2o5/3*b - (contains "2gidhid") o3o5/3x5/2x5/3*b - [Grünbaumian] x3x5/3x5/2o5/3*b - (contains "2gidhid") x3o5/3x5/2x5/3*b - [Grünbaumian] o3x5/3x5/2x5/3*b - [Grünbaumian] x3x5/3x5/2x5/3*b - [Grünbaumian] ``` ```x3/2x5/3o5/2o5/3*b - [Grünbaumian] x3/2o5/3x5/2o5/3*b - (contains "2sissid") o3/2x5/3x5/2o5/3*b - (contains "2gidhid") o3/2o5/3x5/2x5/3*b - [Grünbaumian] x3/2x5/3x5/2o5/3*b - [Grünbaumian] x3/2o5/3x5/2x5/3*b - [Grünbaumian] o3/2x5/3x5/2x5/3*b - [Grünbaumian] x3/2x5/3x5/2x5/3*b - [Grünbaumian] ``` ```x3/2x5/2o5/3o5/3*b - [Grünbaumian] x3/2o5/2x5/3o5/3*b - (contains "2sissid") x3/2o5/2o5/3x5/3*b - (contains "2sissid") o3/2x5/2x5/3o5/3*b - [Grünbaumian] o3/2x5/2o5/3x5/3*b - (contains "2gidhid") o3/2o5/2x5/3x5/3*b - (contains "2gidhid") x3/2x5/2x5/3o5/3*b - [Grünbaumian] x3/2x5/2o5/3x5/3*b - [Grünbaumian] x3/2o5/2x5/3x5/3*b - o3/2x5/2x5/3x5/3*b - [Grünbaumian] x3/2x5/2x5/3x5/3*b - [Grünbaumian] ``` (partial)snubs andholosnubs ```... ``` ```... ``` ```... ```

### Hecatonicosachoral ("hyic") Symmetries – type o5o3o3/2o3*b   (up)

 o5o3o3/2o3*b (µ=2) o5o3o3o3/2*b (µ=118) o5/4o3o3o3/2*b (µ=1082) quasiregulars ```x5o3o3/2o3*b - 2hi (?) (contains f-"2tet" as verf) o5x3o3/2o3*b - (contains "2tet") o5o3x3/2o3*b - (contains "2tet") ``` ```x5o3o3o3/2*b - 2hi (?) (contains f-"2tet" as verf) o5x3o3o3/2*b - (contains "2tet") o5o3x3o3/2*b - (contains "2tet") o5o3o3x3/2*b - (contains "2tet") ``` ```x5/4o3o3o3/2*b - 2hi (?) (contains f-"2tet" as verf) o5/4x3o3o3/2*b - (contains "2tet") o5/4o3x3o3/2*b - (contains "2tet") o5/4o3o3x3/2*b - (contains "2tet") ``` otherWythoffians ```x5x3o3/2o3*b - (contains "2tet") x5o3x3/2o3*b - sirdtapady+600 2tet (contains "2tet") o5x3x3/2o3*b - srawv hixhi o5o3x3/2x3*b - [Grünbaumian] x5x3x3/2o3*b - spixhihy x5o3x3/2x3*b - [Grünbaumian] o5x3x3/2x3*b - [Grünbaumian] x5x3x3/2x3*b - [Grünbaumian] ``` ```x5x3o3o3/2*b - (contains "2tet") x5o3x3o3/2*b - sirdtapady+600 2tet (contains "2tet") x5o3o3x3/2*b - (contains gicdatrid) o5x3x3o3/2*b - srawv hixhi o5x3o3x3/2*b - [Grünbaumian] o5o3x3x3/2*b - 2gifdahihox (?) x5x3x3o3/2*b - spixhihy x5x3o3x3/2*b - [Grünbaumian] x5o3x3x3/2*b - o5x3x3x3/2*b - [Grünbaumian] x5x3x3x3/2*b - [Grünbaumian] ``` ```x5/4x3o3o3/2*b - [Grünbaumian] x5/4o3x3o3/2*b - (contains gicdatrid) x5/4o3o3x3/2*b - sirdtapady+600 2tet (contains "2tet") o5/4x3x3o3/2*b - srawv hixhi o5/4x3o3x3/2*b - [Grünbaumian] o5/4o3x3x3/2*b - 2gifdahihox (?) x5/4x3x3o3/2*b - [Grünbaumian] x5/4x3o3x3/2*b - [Grünbaumian] x5/4o3x3x3/2*b - o5/4x3x3x3/2*b - [Grünbaumian] x5/4x3x3x3/2*b - [Grünbaumian] ``` (partial)snubs andholosnubs ```... ``` ```... ``` ```... ``` o5/4o3o3/2o3*b (µ=1198) o5o3/2o3/2o3/2*b (µ=1202) o5/4o3/2o3/2o3/2*b (µ=2398) quasiregulars ```x5/4o3o3/2o3*b - 2hi (?) (contains f-"2tet" as verf) o5/4x3o3/2o3*b - (contains "2tet") o5/4o3x3/2o3*b - (contains "2tet") ``` ```x5o3/2o3/2o3/2*b - 2hi (?) (contains f-"2tet" as verf) o5x3/2o3/2o3/2*b - (contains "2tet") o5o3/2x3/2o3/2*b - (contains "2tet") ``` ```x5/4o3/2o3/2o3/2*b - 2hi (?) (contains f-"2tet" as verf) o5/4x3/2o3/2o3/2*b - (contains "2tet") o5/4o3/2x3/2o3/2*b - (contains "2tet") ``` otherWythoffians ```x5/4x3o3/2o3*b - [Grünbaumian] x5/4o3x3/2o3*b - (contains gicdatrid) o5/4x3x3/2o3*b - srawv hixhi o5/4o3x3/2x3*b - [Grünbaumian] x5/4x3x3/2o3*b - [Grünbaumian] x5/4o3x3/2x3*b - [Grünbaumian] o5/4x3x3/2x3*b - [Grünbaumian] x5/4x3x3/2x3*b - [Grünbaumian] ``` ```x5x3/2o3/2o3/2*b - (contains "2tet") x5o3/2x3/2o3/2*b - (contains gicdatrid) o5x3/2x3/2o3/2*b - [Grünbaumian] o5o3/2x3/2x3/2*b - [Grünbaumian] x5x3/2x3/2o3/2*b - [Grünbaumian] x5o3/2x3/2x3/2*b - [Grünbaumian] o5x3/2x3/2x3/2*b - [Grünbaumian] x5x3/2x3/2x3/2*b - [Grünbaumian] ``` ```x5/4x3/2o3/2o3/2*b - [Grünbaumian] x5/4o3/2x3/2o3/2*b - sirdtapady+600 2tet (contains "2tet") o5/4x3/2x3/2o3/2*b - [Grünbaumian] o5/4o3/2x3/2x3/2*b - [Grünbaumian] x5/4x3/2x3/2o3/2*b - [Grünbaumian] x5/4o3/2x3/2x3/2*b - [Grünbaumian] o5/4x3/2x3/2x3/2*b - [Grünbaumian] x5/4x3/2x3/2x3/2*b - [Grünbaumian] ``` (partial)snubs andholosnubs ```... ``` ```... ``` ```... ```

### Hecatonicosachoral ("hyic") Symmetries – type o5/2o3o3/2o3*b   (up)

 o5/2o3o3/2o3*b (µ=382) o5/2o3o3o3/2*b (µ=458) o5/3o3o3o3/2*b (µ=742) quasiregulars ```x5/2o3o3/2o3*b - 2gogishi (?) (contains v-"2tet" as verf) o5/2x3o3/2o3*b - (contains "2tet") o5/2o3x3/2o3*b - (contains "2tet") ``` ```x5/2o3o3o3/2*b - 2gogishi (?) (contains v-"2tet" as verf) o5/2x3o3o3/2*b - (contains "2tet") o5/2o3x3o3/2*b - (contains "2tet") o5/2o3o3x3/2*b - (contains "2tet") ``` ```x5/3o3o3o3/2*b - 2gogishi (?) (contains v-"2tet" as verf) o5/3x3o3o3/2*b - (contains "2tet") o5/3o3x3o3/2*b - (contains "2tet") o5/3o3o3x3/2*b - (contains "2tet") ``` otherWythoffians ```x5/2x3o3/2o3*b - [Grünbaumian] x5/2o3x3/2o3*b - (contains sicdatrid) o5/2x3x3/2o3*b - garawv hixhi o5/2o3x3/2x3*b - [Grünbaumian] x5/2x3x3/2o3*b - [Grünbaumian] x5/2o3x3/2x3*b - [Grünbaumian] o5/2x3x3/2x3*b - [Grünbaumian] x5/2x3x3/2x3*b - [Grünbaumian] ``` ```x5/2x3o3o3/2*b - [Grünbaumian] x5/2o3x3o3/2*b - (contains sicdatrid) x5/2o3o3x3/2*b - gadathiphi+600 2tet (contains "2tet") o5/2x3x3o3/2*b - garawv hixhi o5/2x3o3x3/2*b - [Grünbaumian] o5/2o3x3x3/2*b - 2sifdahihox (?) x5/2x3x3o3/2*b - [Grünbaumian] x5/2x3o3x3/2*b - [Grünbaumian] x5/2o3x3x3/2*b - o5/2x3x3x3/2*b - [Grünbaumian] x5/2x3x3x3/2*b - [Grünbaumian] ``` ```x5/3x3o3o3/2*b - (contains "2tet") x5/3o3x3o3/2*b - gadathiphi+600 2tet (contains "2tet") x5/3o3o3x3/2*b - (contains sicdatrid) o5/3x3x3o3/2*b - garawv hixhi o5/3x3o3x3/2*b - [Grünbaumian] o5/3o3x3x3/2*b - 2sifdahihox (?) x5/3x3x3o3/2*b - gippixhihy x5/3x3o3x3/2*b - [Grünbaumian] x5/3o3x3x3/2*b - o5/3x3x3x3/2*b - [Grünbaumian] x5/3x3x3x3/2*b - [Grünbaumian] ``` (partial)snubs andholosnubs ```... ``` ```... ``` ```... ``` o5/3o3o3/2o3*b (µ=818) o5/2o3/2o3/2o3/2*b (µ=1582) o5/3o3/2o3/2o3/2*b (µ=2018) quasiregulars ```x5/3o3o3/2o3*b - 2gogishi (?) (contains v-"2tet" as verf) o5/3x3o3/2o3*b - (contains "2tet") o5/3o3x3/2o3*b - (contains "2tet") ``` ```x5/2o3/2o3/2o3/2*b - 2gogishi (?) (contains v-"2tet" as verf) o5/2x3/2o3/2o3/2*b - (contains "2tet") o5/2o3/2x3/2o3/2*b - (contains "2tet") ``` ```x5/3o3/2o3/2o3/2*b - 2gogishi (?) (contains v-"2tet" as verf) o5/3x3/2o3/2o3/2*b - (contains "2tet") o5/3o3/2x3/2o3/2*b - (contains "2tet") ``` otherWythoffians ```x5/3x3o3/2o3*b - (contains "2tet") x5/3o3x3/2o3*b - gadathiphi+600 2tet (contains "2tet") o5/3x3x3/2o3*b - garawv hixhi o5/3o3x3/2x3*b - [Grünbaumian] x5/3x3x3/2o3*b - gippixhihy x5/3o3x3/2x3*b - [Grünbaumian] o5/3x3x3/2x3*b - [Grünbaumian] x5/3x3x3/2x3*b - [Grünbaumian] ``` ```x5/2x3/2o3/2o3/2*b - [Grünbaumian] x5/2o3/2x3/2o3/2*b - gadathiphi+600 2tet (contains "2tet") o5/2x3/2x3/2o3/2*b - [Grünbaumian] o5/2o3/2x3/2x3/2*b - [Grünbaumian] x5/2x3/2x3/2o3/2*b - [Grünbaumian] x5/2o3/2x3/2x3/2*b - [Grünbaumian] o5/2x3/2x3/2x3/2*b - [Grünbaumian] x5/2x3/2x3/2x3/2*b - [Grünbaumian] ``` ```x5/3x3/2o3/2o3/2*b - (contains "2tet") x5/3o3/2x3/2o3/2*b - (contains sicdatrid) o5/3x3/2x3/2o3/2*b - [Grünbaumian] o5/3o3/2x3/2x3/2*b - [Grünbaumian] x5/3x3/2x3/2o3/2*b - [Grünbaumian] x5/3o3/2x3/2x3/2*b - [Grünbaumian] o5/3x3/2x3/2x3/2*b - [Grünbaumian] x5/3x3/2x3/2x3/2*b - [Grünbaumian] ``` (partial)snubs andholosnubs ```... ``` ```... ``` ```... ```

### Hecatonicosachoral ("hyic") Symmetries – type o5o3o5/4o3*b   (up)

 o5o3o5/4o3*b (µ=40) o5o3o5o3/2*b (µ=80) o5/4o3o5o3/2*b (µ=640) quasiregulars ```x5o3o5/4o3*b - 2gahi (?) (contains f-"2gike" as verf) o5x3o5/4o3*b - (contains "2gike") o5o3x5/4o3*b - gitpodady ``` ```x5o3o5o3/2*b - 2gahi (?) (contains f-"2gike" as verf) o5x3o5o3/2*b - (contains "2gike") o5o3x5o3/2*b - gitpodady o5o3o5x3/2*b - gitpodady ``` ```x5/4o3o5o3/2*b - 2gahi (?) (contains f-"2gike" as verf) o5/4x3o5o3/2*b - (contains "2gike") o5/4o3x5o3/2*b - gitpodady o5/4o3o5x3/2*b - gitpodady ``` otherWythoffians ```x5x3o5/4o3*b - (contains "2gike") x5o3x5/4o3*b - sedit pathi o5x3x5/4o3*b - grawvathi o5o3x5/4x3*b - [Grünbaumian] x5x3x5/4o3*b - ghipady x5o3x5/4x3*b - [Grünbaumian] o5x3x5/4x3*b - [Grünbaumian] x5x3x5/4x3*b - [Grünbaumian] ``` ```x5x3o5o3/2*b - (contains "2gike") x5o3x5o3/2*b - sedit pathi x5o3o5x3/2*b - (contains gicdatrid) o5x3x5o3/2*b - grawvathi o5x3o5x3/2*b - [Grünbaumian] o5o3x5x3/2*b - (contains "2seihid") x5x3x5o3/2*b - ghipady x5x3o5x3/2*b - [Grünbaumian] x5o3x5x3/2*b - o5x3x5x3/2*b - [Grünbaumian] x5x3x5x3/2*b - [Grünbaumian] ``` ```x5/4x3o5o3/2*b - [Grünbaumian] x5/4o3x5o3/2*b - (contains gicdatrid) x5/4o3o5x3/2*b - sedit pathi o5/4x3x5o3/2*b - grawvathi o5/4x3o5x3/2*b - [Grünbaumian] o5/4o3x5x3/2*b - (contains "2seihid") x5/4x3x5o3/2*b - [Grünbaumian] x5/4x3o5x3/2*b - [Grünbaumian] x5/4o3x5x3/2*b - o5/4x3x5x3/2*b - [Grünbaumian] x5/4x3x5x3/2*b - [Grünbaumian] ``` (partial)snubs andholosnubs ```... ``` ```... ``` ```... ``` o5o3/2o5/4o3/2*b (µ=1240) o5/4o3o5/4o3*b (µ=1640) o5/4o3/2o5/4o3/2*b (µ=2840) quasiregulars ```x5o3/2o5/4o3/2*b - 2gahi (?) (contains f-"2gike" as verf) o5x3/2o5/4o3/2*b - (contains "2gike") o5o3/2x5/4o3/2*b - gitpodady ``` ```x5/4o3o5/4o3*b - 2gahi (?) (contains f-"2gike" as verf) o5/4x3o5/4o3*b - (contains "2gike") o5/4o3x5/4o3*b - gitpodady ``` ```x5/4o3/2o5/4o3/2*b - 2gahi (?) (contains f-"2gike" as verf) o5/4x3/2o5/4o3/2*b - (contains "2gike") o5/4o3/2x5/4o3/2*b - gitpodady ``` otherWythoffians ```x5x3/2o5/4o3/2*b - (contains "2gike") x5o3/2x5/4o3/2*b - (contains gicdatrid) o5x3/2x5/4o3/2*b - [Grünbaumian] o5o3/2x5/4x3/2*b - [Grünbaumian] x5x3/2x5/4o3/2*b - [Grünbaumian] x5o3/2x5/4x3/2*b - [Grünbaumian] o5x3/2x5/4x3/2*b - [Grünbaumian] x5x3/2x5/4x3/2*b - [Grünbaumian] ``` ```x5/4x3o5/4o3*b - [Grünbaumian] x5/4o3x5/4o3*b - (contains gicdatrid) o5/4x3x5/4o3*b - grawvathi o5/4o3x5/4x3*b - [Grünbaumian] x5/4x3x5/4o3*b - [Grünbaumian] x5/4o3x5/4x3*b - [Grünbaumian] o5/4x3x5/4x3*b - [Grünbaumian] x5/4x3x5/4x3*b - [Grünbaumian] ``` ```x5/4x3/2o5/4o3/2*b - [Grünbaumian] x5/4o3/2x5/4o3/2*b - sedit pathi o5/4x3/2x5/4o3/2*b - [Grünbaumian] o5/4o3/2x5/4x3/2*b - [Grünbaumian] x5/4x3/2x5/4o3/2*b - [Grünbaumian] x5/4o3/2x5/4x3/2*b - [Grünbaumian] o5/4x3/2x5/4x3/2*b - [Grünbaumian] x5/4x3/2x5/4x3/2*b - [Grünbaumian] ``` (partial)snubs andholosnubs ```... ``` ```... ``` ```... ```

### Hecatonicosachoral ("hyic") Symmetries – type o5/2o3o5/2o3*b   (up)

 o5/2o3o5/2o3*b (µ=40) o5/3o3o5/2o3*b (µ=200) o5/2o3o5/3o3/2*b (µ=800) quasiregulars ```x5/2o3o5/2o3*b - 2gishi (?) (contains v-"2ike" as verf) o5/2x3o5/2o3*b - (contains "2ike") o5/2o3x5/2o3*b - sitpodady ``` ```x5/3o3o5/2o3*b - 2gishi (?) (contains v-"2ike" as verf) o5/3x3o5/2o3*b - (contains "2ike") o5/3o3x5/2o3*b - sitpodady ``` ```x5/2o3o5/3o3/2*b - 2gishi (?) (contains v-"2ike" as verf) o5/2x3o5/3o3/2*b - (contains "2ike") o5/2o3x5/3o3/2*b - sitpodady o5/2o3o5/3x3/2*b - sitpodady ``` otherWythoffians ```x5/2x3o5/2o3*b - [Grünbaumian] x5/2o3x5/2o3*b - (contains sicdatrid) o5/2x3x5/2o3*b - swavathi o5/2o3x5/2x3*b - [Grünbaumian] x5/2x3x5/2o3*b - [Grünbaumian] x5/2o3x5/2x3*b - [Grünbaumian] o5/2x3x5/2x3*b - [Grünbaumian] x5/2x3x5/2x3*b - [Grünbaumian] ``` ```x5/3x3o5/2o3*b - (contains "2ike") x5/3o3x5/2o3*b - gaedit pathi o5/3x3x5/2o3*b - swavathi o5/3o3x5/2x3*b - [Grünbaumian] x5/3x3x5/2o3*b - shipady x5/3o3x5/2x3*b - [Grünbaumian] o5/3x3x5/2x3*b - [Grünbaumian] x5/3x3x5/2x3*b - [Grünbaumian] ``` ```x5/2x3o5/3o3/2*b - [Grünbaumian] x5/2o3x5/3o3/2*b - (contains sicdatrid) x5/2o3o5/3x3/2*b - gaedit pathi o5/2x3x5/3o3/2*b - swavathi o5/2x3o5/3x3/2*b - [Grünbaumian] o5/2o3x5/3x3/2*b - (contains "2geihid") x5/2x3x5/3o3/2*b - [Grünbaumian] x5/2x3o5/3x3/2*b - [Grünbaumian] x5/2o3x5/3x3/2*b - o5/2x3x5/3x3/2*b - [Grünbaumian] x5/2x3x5/3x3/2*b - [Grünbaumian] ``` (partial)snubs andholosnubs ```... ``` ```... ``` ```... ``` o5/2o3/2o5/2o3/2*b (µ=1240) o5/3o3o5/3o3/2*b (µ=1360) o5/3o3/2o5/2o3/2*b (µ=1400) quasiregulars ```x5/2o3/2o5/2o3/2*b - 2gishi (?) (contains v-"2ike" as verf) o5/2x3/2o5/2o3/2*b - (contains "2ike") o5/2o3/2x5/2o3/2*b - sitpodady ``` ```x5/3o3o5/3o3/2*b - 2gishi (?) (contains v-"2ike" as verf) o5/3x3o5/3o3/2*b - (contains "2ike") o5/3o3x5/3o3/2*b - sitpodady o5/3o3o5/3x3/2*b - sitpodady ``` ```x5/3o3/2o5/2o3/2*b - 2gishi (?) (contains v-"2ike" as verf) o5/3x3/2o5/2o3/2*b - (contains "2ike") o5/3o3/2x5/2o3/2*b - sitpodady ``` otherWythoffians ```x5/2x3/2o5/2o3/2*b - [Grünbaumian] x5/2o3/2x5/2o3/2*b - gaedit pathi o5/2x3/2x5/2o3/2*b - [Grünbaumian] o5/2o3/2x5/2x3/2*b - [Grünbaumian] x5/2x3/2x5/2o3/2*b - [Grünbaumian] x5/2o3/2x5/2x3/2*b - [Grünbaumian] o5/2x3/2x5/2x3/2*b - [Grünbaumian] x5/2x3/2x5/2x3/2*b - [Grünbaumian] ``` ```x5/3x3o5/3o3/2*b - (contains "2ike") x5/3o3x5/3o3/2*b - gaedit pathi x5/3o3o5/3x3/2*b - (contains sicdatrid) o5/3x3x5/3o3/2*b - swavathi o5/3x3o5/3x3/2*b - [Grünbaumian] o5/3o3x5/3x3/2*b - (contains "2geihid") x5/3x3x5/3o3/2*b - shipady x5/3x3o5/3x3/2*b - [Grünbaumian] x5/3o3x5/3x3/2*b - o5/3x3x5/3x3/2*b - [Grünbaumian] x5/3x3x5/3x3/2*b - [Grünbaumian] ``` ```x5/3x3/2o5/2o3/2*b - (contains "2ike") x5/3o3/2x5/2o3/2*b - (contains sicdatrid) o5/3x3/2x5/2o3/2*b - [Grünbaumian] o5/3o3/2x5/2x3/2*b - [Grünbaumian] x5/3x3/2x5/2o3/2*b - [Grünbaumian] x5/3o3/2x5/2x3/2*b - [Grünbaumian] o5/3x3/2x5/2x3/2*b - [Grünbaumian] x5/3x3/2x5/2x3/2*b - [Grünbaumian] ``` (partial)snubs andholosnubs ```... ``` ```... ``` ```... ```

### Hecatonicosachoral ("hyic") Symmetries – type o5o3o5o5/3*b   (up)

 o5o3o5o5/3*b (µ=14) o5o3o5/4o5/2*b (µ=106) o5o3/2o5o5/2*b (µ=254) o5/4o3o5o5/3*b (µ=466) quasiregulars ```x5o3o5o5/3*b - gahi+gohi (?) (contains f-gacid as verf) o5x3o5o5/3*b - (contains gacid) o5o3x5o5/3*b - (contains cid) o5o3o5x5/3*b - sishi+idhi (?) ``` ```x5o3o5/4o5/2*b - gahi+gohi (?) (contains f-gacid as verf) o5x3o5/4o5/2*b - (contains gacid) o5o3x5/4o5/2*b - (contains cid) o5o3o5/4x5/2*b - sishi+idhi (?) ``` ```x5o3/2o5o5/2*b - gahi+gohi (?) (contains f-gacid as verf) o5x3/2o5o5/2*b - (contains gacid) o5o3/2x5o5/2*b - (contains cid) o5o3/2o5x5/2*b - sishi+idhi (?) ``` ```x5/4o3o5o5/3*b - gahi+gohi (?) (contains f-gacid as verf) o5/4x3o5o5/3*b - (contains gacid) o5/4o3x5o5/3*b - (contains cid) o5/4o3o5x5/3*b - sishi+idhi (?) ``` otherWythoffians ```x5x3o5o5/3*b - (contains gacid) x5o3x5o5/3*b - (contains cid) x5o3o5x5/3*b - (contains cadditradid) o5x3x5o5/3*b - srawv hidy o5x3o5x5/3*b - swav ditathi o5o3x5x5/3*b - sisdipthi x5x3x5o5/3*b - siphidy x5x3o5x5/3*b - gid thipady x5o3x5x5/3*b - o5x3x5x5/3*b - dahiquatady x5x3x5x5/3*b - sidhiquit paddy ``` ```x5x3o5/4o5/2*b - (contains gacid) x5o3x5/4o5/2*b - (contains cid) x5o3o5/4x5/2*b - seedatepthi o5x3x5/4o5/2*b - srawv hidy o5x3o5/4x5/2*b - [Grünbaumian] o5o3x5/4x5/2*b - [Grünbaumian] x5x3x5/4o5/2*b - siphidy x5x3o5/4x5/2*b - [Grünbaumian] x5o3x5/4x5/2*b - [Grünbaumian] o5x3x5/4x5/2*b - [Grünbaumian] x5x3x5/4x5/2*b - [Grünbaumian] ``` ```x5x3/2o5o5/2*b - (contains gacid) x5o3/2x5o5/2*b - (contains cid) x5o3/2o5x5/2*b - seedatepthi o5x3/2x5o5/2*b - [Grünbaumian] o5x3/2o5x5/2*b - [Grünbaumian] o5o3/2x5x5/2*b - sisdipthi x5x3/2x5o5/2*b - [Grünbaumian] x5x3/2o5x5/2*b - [Grünbaumian] x5o3/2x5x5/2*b - o5x3/2x5x5/2*b - [Grünbaumian] x5x3/2x5x5/2*b - [Grünbaumian] ``` ```x5/4x3o5o5/3*b - [Grünbaumian] x5/4o3x5o5/3*b - (contains cid) x5/4o3o5x5/3*b - seedatepthi o5/4x3x5o5/3*b - srawv hidy o5/4x3o5x5/3*b - swav ditathi o5/4o3x5x5/3*b - sisdipthi x5/4x3x5o5/3*b - [Grünbaumian] x5/4x3o5x5/3*b - [Grünbaumian] x5/4o3x5x5/3*b - o5/4x3x5x5/3*b - dahiquatady x5/4x3x5x5/3*b - [Grünbaumian] ``` (partial)snubs andholosnubs ```... ``` ```... ``` ```... ``` ```... ``` o5/4o3/2o5o5/2*b (µ=706) o5o3/2o5/4o5/3*b (µ=1066) o5/4o3o5/4o5/2*b (µ=1814) o5/4o3/2o5/4o5/3*b (µ=2774) quasiregulars ```x5/4o3/2o5o5/2*b - gahi+gohi (?) (contains f-gacid as verf) o5/4x3/2o5o5/2*b - (contains gacid) o5/4o3/2x5o5/2*b - (contains cid) o5/4o3/2o5x5/2*b - sishi+idhi (?) ``` ```x5o3/2o5/4o5/3*b - gahi+gohi (?) (contains f-gacid as verf) o5x3/2o5/4o5/3*b - (contains gacid) o5o3/2x5/4o5/3*b - (contains cid) o5o3/2o5/4x5/3*b - sishi+idhi (?) ``` ```x5/4o3o5/4o5/2*b - gahi+gohi (?) (contains f-gacid as verf) o5/4x3o5/4o5/2*b - (contains gacid) o5/4o3x5/4o5/2*b - (contains cid) o5/4o3o5/4x5/2*b - sishi+idhi (?) ``` ```x5/4o3/2o5/4o5/3*b - gahi+gohi (?) (contains f-gacid as verf) o5/4x3/2o5/4o5/3*b - (contains gacid) o5/4o3/2x5/4o5/3*b - (contains cid) o5/4o3/2o5/4x5/3*b - sishi+idhi (?) ``` otherWythoffians ```x5/4x3/2o5o5/2*b - [Grünbaumian] x5/4o3/2x5o5/2*b - (contains cid) x5/4o3/2o5x5/2*b - (contains cadditradid) o5/4x3/2x5o5/2*b - [Grünbaumian] o5/4x3/2o5x5/2*b - [Grünbaumian] o5/4o3/2x5x5/2*b - sisdipthi x5/4x3/2x5o5/2*b - [Grünbaumian] x5/4x3/2o5x5/2*b - [Grünbaumian] x5/4o3/2x5x5/2*b - o5/4x3/2x5x5/2*b - [Grünbaumian] x5/4x3/2x5x5/2*b - [Grünbaumian] ``` ```x5x3/2o5/4o5/3*b - (contains gacid) x5o3/2x5/4o5/3*b - (contains cid) x5o3/2o5/4x5/3*b - (contains cadditradid) o5x3/2x5/4o5/3*b - [Grünbaumian] o5x3/2o5/4x5/3*b - swav ditathi o5o3/2x5/4x5/3*b - [Grünbaumian] x5x3/2x5/4o5/3*b - [Grünbaumian] x5x3/2o5/4x5/3*b - gid thipady x5o3/2x5/4x5/3*b - [Grünbaumian] o5x3/2x5/4x5/3*b - [Grünbaumian] x5x3/2x5/4x5/3*b - [Grünbaumian] ``` ```x5/4x3o5/4o5/2*b - [Grünbaumian] x5/4o3x5/4o5/2*b - (contains cid) x5/4o3o5/4x5/2*b - (contains cadditradid) o5/4x3x5/4o5/2*b - srawv hidy o5/4x3o5/4x5/2*b - [Grünbaumian] o5/4o3x5/4x5/2*b - [Grünbaumian] x5/4x3x5/4o5/2*b - [Grünbaumian] x5/4x3o5/4x5/2*b - [Grünbaumian] x5/4o3x5/4x5/2*b - [Grünbaumian] o5/4x3x5/4x5/2*b - [Grünbaumian] x5/4x3x5/4x5/2*b - [Grünbaumian] ``` ```x5/4x3/2o5/4o5/3*b - [Grünbaumian] x5/4o3/2x5/4o5/3*b - (contains cid) x5/4o3/2o5/4x5/3*b - seedatepthi o5/4x3/2x5/4o5/3*b - [Grünbaumian] o5/4x3/2o5/4x5/3*b - swav ditathi o5/4o3/2x5/4x5/3*b - [Grünbaumian] x5/4x3/2x5/4o5/3*b - [Grünbaumian] x5/4x3/2o5/4x5/3*b - [Grünbaumian] x5/4o3/2x5/4x5/3*b - [Grünbaumian] o5/4x3/2x5/4x5/3*b - [Grünbaumian] x5/4x3/2x5/4x5/3*b - [Grünbaumian] ``` (partial)snubs andholosnubs ```... ``` ```... ``` ```... ``` ```... ```

### Hecatonicosachoral ("hyic") Symmetries – type o5/2o3o5/3o5*b   (up)

 o5/2o3o5/3o5*b (µ=86) o5/2o3/2o5/2o5*b (µ=274) o5/3o3o5/3o5*b (µ=394) o5/3o3/2o5/2o5*b (µ=686) quasiregulars ```x5/2o3o5/3o5*b - gishi+gashi (?) (contains v-cid as verf) o5/2x3o5/3o5*b - (contains cid) o5/2o3x5/3o5*b - (contains gacid) o5/2o3o5/3x5*b - gaghi+idhi (?) ``` ```x5/2o3/2o5/2o5*b - gishi+gashi (?) (contains v-cid as verf) o5/2x3/2o5/2o5*b - (contains cid) o5/2o3/2x5/2o5*b - (contains gacid) o5/2o3/2o5/2x5*b - gaghi+idhi (?) ``` ```x5/3o3o5/3o5*b - gishi+gashi (?) (contains v-cid as verf) o5/3x3o5/3o5*b - (contains cid) o5/3o3x5/3o5*b - (contains gacid) o5/3o3o5/3x5*b - gaghi+idhi (?) ``` ```x5/3o3/2o5/2o5*b - gishi+gashi (?) (contains v-cid as verf) o5/3x3/2o5/2o5*b - (contains cid) o5/3o3/2x5/2o5*b - (contains gacid) o5/3o3/2o5/2x5*b - gaghi+idhi (?) ``` otherWythoffians ```x5/2x3o5/3o5*b - [Grünbaumian] x5/2o3x5/3o5*b - (contains gacid) x5/2o3o5/3x5*b - geedatepthi o5/2x3x5/3o5*b - grawv hidy o5/2x3o5/3x5*b - grawv ditathi o5/2o3x5/3x5*b - gisdipthi x5/2x3x5/3o5*b - [Grünbaumian] x5/2x3o5/3x5*b - [Grünbaumian] x5/2o3x5/3x5*b - o5/2x3x5/3x5*b - dahitady x5/2x3x5/3x5*b - [Grünbaumian] ``` ```x5/2x3/2o5/2o5*b - [Grünbaumian] x5/2o3/2x5/2o5*b - (contains gacid) x5/2o3/2o5/2x5*b - geedatepthi o5/2x3/2x5/2o5*b - [Grünbaumian] o5/2x3/2o5/2x5*b - grawv ditathi o5/2o3/2x5/2x5*b - [Grünbaumian] x5/2x3/2x5/2o5*b - [Grünbaumian] x5/2x3/2o5/2x5*b - [Grünbaumian] x5/2o3/2x5/2x5*b - [Grünbaumian] o5/2x3/2x5/2x5*b - [Grünbaumian] x5/2x3/2x5/2x5*b - [Grünbaumian] ``` ```x5/3x3o5/3o5*b - (contains cid) x5/3o3x5/3o5*b - (contains gacid) x5/3o3o5/3x5*b - (contains cadditradid) o5/3x3x5/3o5*b - grawv hidy o5/3x3o5/3x5*b - grawv ditathi o5/3o3x5/3x5*b - gisdipthi x5/3x3x5/3o5*b - giphidy x5/3x3o5/3x5*b - sid thipady x5/3o3x5/3x5*b - o5/3x3x5/3x5*b - dahitady x5/3x3x5/3x5*b - gidhiquit paddy ``` ```x5/3x3/2o5/2o5*b - (contains cid) x5/3o3/2x5/2o5*b - (contains gacid) x5/3o3/2o5/2x5*b - (contains cadditradid) o5/3x3/2x5/2o5*b - [Grünbaumian] o5/3x3/2o5/2x5*b - grawv ditathi o5/3o3/2x5/2x5*b - [Grünbaumian] x5/3x3/2x5/2o5*b - [Grünbaumian] x5/3x3/2o5/2x5*b - sid thipady x5/3o3/2x5/2x5*b - [Grünbaumian] o5/3x3/2x5/2x5*b - [Grünbaumian] x5/3x3/2x5/2x5*b - [Grünbaumian] ``` (partial)snubs andholosnubs ```... ``` ```... ``` ```... ``` ```... ``` o5/2o3o5/2o5/4*b (µ=754) o5/3o3o5/2o5/4*b (µ=1166) o5/2o3/2o5/3o5/4*b (µ=1766) o5/3o3/2o5/3o5/4*b (µ=2074) quasiregulars ```x5/2o3o5/2o5/4*b - gishi+gashi (?) (contains v-cid as verf) o5/2x3o5/2o5/4*b - (contains cid) o5/2o3x5/2o5/4*b - (contains gacid) o5/2o3o5/2x5/4*b - gaghi+idhi (?) ``` ```x5/3o3o5/2o5/4*b - gishi+gashi (?) (contains v-cid as verf) o5/3x3o5/2o5/4*b - (contains cid) o5/3o3x5/2o5/4*b - (contains gacid) o5/3o3o5/2x5/4*b - gaghi+idhi (?) ``` ```x5/2o3/2o5/3o5/4*b - gishi+gashi (?) (contains v-cid as verf) o5/2x3/2o5/3o5/4*b - (contains cid) o5/2o3/2x5/3o5/4*b - (contains gacid) o5/2o3/2o5/3x5/4*b - gaghi+idhi (?) ``` ```x5/3o3/2o5/3o5/4*b - gishi+gashi (?) (contains v-cid as verf) o5/3x3/2o5/3o5/4*b - (contains cid) o5/3o3/2x5/3o5/4*b - (contains gacid) o5/3o3/2o5/3x5/4*b - gaghi+idhi (?) ``` otherWythoffians ```x5/2x3o5/2o5/4*b - [Grünbaumian] x5/2o3x5/2o5/4*b - (contains gacid) x5/2o3o5/2x5/4*b - (contains cadditradid) o5/2x3x5/2o5/4*b - grawv hidy o5/2x3o5/2x5/4*b - [Grünbaumian] o5/2o3x5/2x5/4*b - [Grünbaumian] x5/2x3x5/2o5/4*b - [Grünbaumian] x5/2x3o5/2x5/4*b - [Grünbaumian] x5/2o3x5/2x5/4*b - [Grünbaumian] o5/2x3x5/2x5/4*b - [Grünbaumian] x5/2x3x5/2x5/4*b - [Grünbaumian] ``` ```x5/3x3o5/2o5/4*b - (contains cid) x5/3o3x5/2o5/4*b - (contains gacid) x5/3o3o5/2x5/4*b - geedatepthi o5/3x3x5/2o5/4*b - grawv hidy o5/3x3o5/2x5/4*b - [Grünbaumian] o5/3o3x5/2x5/4*b - [Grünbaumian] x5/3x3x5/2o5/4*b - giphidy x5/3x3o5/2x5/4*b - [Grünbaumian] x5/3o3x5/2x5/4*b - [Grünbaumian] o5/3x3x5/2x5/4*b - [Grünbaumian] x5/3x3x5/2x5/4*b - [Grünbaumian] ``` ```x5/2x3/2o5/3o5/4*b - [Grünbaumian] x5/2o3/2x5/3o5/4*b - (contains gacid) x5/2o3/2o5/3x5/4*b - (contains cadditradid) o5/2x3/2x5/3o5/4*b - [Grünbaumian] o5/2x3/2o5/3x5/4*b - [Grünbaumian] o5/2o3/2x5/3x5/4*b - gisdipthi x5/2x3/2x5/3o5/4*b - [Grünbaumian] x5/2x3/2o5/3x5/4*b - [Grünbaumian] x5/2o3/2x5/3x5/4*b - o5/2x3/2x5/3x5/4*b - [Grünbaumian] x5/2x3/2x5/3x5/4*b - [Grünbaumian] ``` ```x5/3x3/2o5/3o5/4*b - (contains cid) x5/3o3/2x5/3o5/4*b - (contains gacid) x5/3o3/2o5/3x5/4*b - geedatepthi o5/3x3/2x5/3o5/4*b - [Grünbaumian] o5/3x3/2o5/3x5/4*b - [Grünbaumian] o5/3o3/2x5/3x5/4*b - gisdipthi x5/3x3/2x5/3o5/4*b - [Grünbaumian] x5/3x3/2o5/3x5/4*b - [Grünbaumian] x5/3o3/2x5/3x5/4*b - o5/3x3/2x5/3x5/4*b - [Grünbaumian] x5/3x3/2x5/3x5/4*b - [Grünbaumian] ``` (partial)snubs andholosnubs ```... ``` ```... ``` ```... ``` ```... ```

### Hecatonicosachoral ("hyic") Symmetries – type o5o3o5/3o5/2*b   (up)

 o5o3o5/3o5/2*b (µ=26) o5o3o5/2o5/3*b (µ=94) o5o3/2o5/2o5/2*b (µ=334) o5o3/2o5/3o5/3*b (µ=986) quasiregulars ```x5o3o5/3o5/2*b - gahi+gohi (?) (contains f-gacid as verf) o5x3o5/3o5/2*b - (contains gacid) o5o3x5/3o5/2*b - (contains gacid) o5o3o5/3x5/2*b - (contains "2gissid") ``` ```x5o3o5/2o5/3*b - gahi+gohi (?) (contains f-gacid as verf) o5x3o5/2o5/3*b - (contains gacid) o5o3x5/2o5/3*b - (contains gacid) o5o3o5/2x5/3*b - (contains "2gissid") ``` ```x5o3/2o5/2o5/2*b - gahi+gohi (?) (contains f-gacid as verf) o5x3/2o5/2o5/2*b - (contains gacid) o5o3/2x5/2o5/2*b - (contains gacid) o5o3/2o5/2x5/2*b - (contains "2gissid") ``` ```x5o3/2o5/3o5/3*b - gahi+gohi (?) (contains f-gacid as verf) o5x3/2o5/3o5/3*b - (contains gacid) o5o3/2x5/3o5/3*b - (contains gacid) o5o3/2o5/3x5/3*b - (contains "2gissid") ``` otherWythoffians ```x5x3o5/3o5/2*b - (contains gacid) x5o3x5/3o5/2*b - (contains gacid) x5o3o5/3x5/2*b - (contains "2gissid") o5x3x5/3o5/2*b - (contains "2sidhei") o5x3o5/3x5/2*b - [Grünbaumian] o5o3x5/3x5/2*b - gidipthi x5x3x5/3o5/2*b - (contains "2sidhei") x5x3o5/3x5/2*b - [Grünbaumian] x5o3x5/3x5/2*b - sik vipathi o5x3x5/3x5/2*b - [Grünbaumian] x5x3x5/3x5/2*b - [Grünbaumian] ``` ```x5x3o5/2o5/3*b - (contains gacid) x5o3x5/2o5/3*b - (contains gacid) x5o3o5/2x5/3*b - (contains "2gissid") o5x3x5/2o5/3*b - (contains "2sidhei") o5x3o5/2x5/3*b - wavathi o5o3x5/2x5/3*b - [Grünbaumian] x5x3x5/2o5/3*b - (contains "2sidhei") x5x3o5/2x5/3*b - mipthi x5o3x5/2x5/3*b - [Grünbaumian] o5x3x5/2x5/3*b - [Grünbaumian] x5x3x5/2x5/3*b - [Grünbaumian] ``` ```x5x3/2o5/2o5/2*b - (contains gacid) x5o3/2x5/2o5/2*b - (contains gacid) x5o3/2o5/2x5/2*b - (contains "2gissid") o5x3/2x5/2o5/2*b - [Grünbaumian] o5x3/2o5/2x5/2*b - [Grünbaumian] o5o3/2x5/2x5/2*b - [Grünbaumian] x5x3/2x5/2o5/2*b - [Grünbaumian] x5x3/2o5/2x5/2*b - [Grünbaumian] x5o3/2x5/2x5/2*b - [Grünbaumian] o5x3/2x5/2x5/2*b - [Grünbaumian] x5x3/2x5/2x5/2*b - [Grünbaumian] ``` ```x5x3/2o5/3o5/3*b - (contains gacid) x5o3/2x5/3o5/3*b - (contains gacid) x5o3/2o5/3x5/3*b - (contains "2gissid") o5x3/2x5/3o5/3*b - [Grünbaumian] o5x3/2o5/3x5/3*b - wavathi o5o3/2x5/3x5/3*b - gidipthi x5x3/2x5/3o5/3*b - [Grünbaumian] x5x3/2o5/3x5/3*b - mipthi x5o3/2x5/3x5/3*b - o5x3/2x5/3x5/3*b - [Grünbaumian] x5x3/2x5/3x5/3*b - [Grünbaumian] ``` (partial)snubs andholosnubs ```... ``` ```... ``` ```... ``` ```... ``` o5/4o3o5/2o5/3*b (µ=1106) o5/4o3o5/3o5/2*b (µ=1174) o5/4o3/2o5/2o5/2*b (µ=1346) o5/4o3/2o5/3o5/3*b (µ=2134) quasiregulars ```x5/4o3o5/2o5/3*b - gahi+gohi (?) (contains f-gacid as verf) o5/4x3o5/2o5/3*b - (contains gacid) o5/4o3x5/2o5/3*b - (contains gacid) o5/4o3o5/2x5/3*b - (contains "2gissid") ``` ```x5/4o3o5/3o5/2*b - gahi+gohi (?) (contains f-gacid as verf) o5/4x3o5/3o5/2*b - (contains gacid) o5/4o3x5/3o5/2*b - (contains gacid) o5/4o3o5/3x5/2*b - (contains "2gissid") ``` ```x5/4o3/2o5/2o5/2*b - gahi+gohi (?) (contains f-gacid as verf) o5/4x3/2o5/2o5/2*b - (contains gacid) o5/4o3/2x5/2o5/2*b - (contains gacid) o5/4o3/2o5/2x5/2*b - (contains "2gissid") ``` ```x5/4o3/2o5/3o5/3*b - gahi+gohi (?) (contains f-gacid as verf) o5/4x3/2o5/3o5/3*b - (contains gacid) o5/4o3/2x5/3o5/3*b - (contains gacid) o5/4o3/2o5/3x5/3*b - (contains "2gissid") ``` otherWythoffians ```x5/4x3o5/2o5/3*b - [Grünbaumian] x5/4o3x5/2o5/3*b - (contains gacid) x5/4o3o5/2x5/3*b - (contains "2gissid") o5/4x3x5/2o5/3*b - (contains "2sidhei") o5/4x3o5/2x5/3*b - wavathi o5/4o3x5/2x5/3*b - [Grünbaumian] x5/4x3x5/2o5/3*b - [Grünbaumian] x5/4x3o5/2x5/3*b - [Grünbaumian] x5/4o3x5/2x5/3*b - [Grünbaumian] o5/4x3x5/2x5/3*b - [Grünbaumian] x5/4x3x5/2x5/3*b - [Grünbaumian] ``` ```x5/4x3o5/3o5/2*b - [Grünbaumian] x5/4o3x5/3o5/2*b - (contains gacid) x5/4o3o5/3x5/2*b - (contains "2gissid") o5/4x3x5/3o5/2*b - (contains "2sidhei") o5/4x3o5/3x5/2*b - [Grünbaumian] o5/4o3x5/3x5/2*b - gidipthi x5/4x3x5/3o5/2*b - [Grünbaumian] x5/4x3o5/3x5/2*b - [Grünbaumian] x5/4o3x5/3x5/2*b - o5/4x3x5/3x5/2*b - [Grünbaumian] x5/4x3x5/3x5/2*b - [Grünbaumian] ``` ```x5/4x3/2o5/2o5/2*b - [Grünbaumian] x5/4o3/2x5/2o5/2*b - (contains gacid) x5/4o3/2o5/2x5/2*b - (contains "2gissid") o5/4x3/2x5/2o5/2*b - [Grünbaumian] o5/4x3/2o5/2x5/2*b - [Grünbaumian] o5/4o3/2x5/2x5/2*b - [Grünbaumian] x5/4x3/2x5/2o5/2*b - [Grünbaumian] x5/4x3/2o5/2x5/2*b - [Grünbaumian] x5/4o3/2x5/2x5/2*b - [Grünbaumian] o5/4x3/2x5/2x5/2*b - [Grünbaumian] x5/4x3/2x5/2x5/2*b - [Grünbaumian] ``` ```x5/4x3/2o5/3o5/3*b - [Grünbaumian] x5/4o3/2x5/3o5/3*b - (contains gacid) x5/4o3/2o5/3x5/3*b - (contains "2gissid") o5/4x3/2x5/3o5/3*b - [Grünbaumian] o5/4x3/2o5/3x5/3*b - wavathi o5/4o3/2x5/3x5/3*b - gidipthi x5/4x3/2x5/3o5/3*b - [Grünbaumian] x5/4x3/2o5/3x5/3*b - [Grünbaumian] x5/4o3/2x5/3x5/3*b - sik vipathi o5/4x3/2x5/3x5/3*b - [Grünbaumian] x5/4x3/2x5/3x5/3*b - [Grünbaumian] ``` (partial)snubs andholosnubs ```... ``` ```... ``` ```... ``` ```... ```

### Hecatonicosachoral ("hyic") Symmetries – type o5/2o3/2o5o5*b   (up)

 o5/2o3/2o5o5*b (µ=46) o5/3o3/2o5o5*b (µ=194) o5/2o3o5/4o5*b (µ=314) o5/2o3o5o5/4*b (µ=526) quasiregulars ```x5/2o3/2o5o5*b - gishi+gashi (?) (contains v-cid as verf) o5/2x3/2o5o5*b - (contains cid) o5/2o3/2x5o5*b - (contains cid) o5/2o3/2o5x5*b - (contains "2doe") ``` ```x5/3o3/2o5o5*b - gishi+gashi (?) (contains v-cid as verf) o5/3x3/2o5o5*b - (contains cid) o5/3o3/2x5o5*b - (contains cid) o5/3o3/2o5x5*b - (contains "2doe") ``` ```x5/2o3o5/4o5*b - gishi+gashi (?) (contains v-cid as verf) o5/2x3o5/4o5*b - (contains cid) o5/2o3x5/4o5*b - (contains cid) o5/2o3o5/4x5*b - (contains "2doe") ``` ```x5/2o3o5o5/4*b - gishi+gashi (?) (contains v-cid as verf) o5/2x3o5o5/4*b - (contains cid) o5/2o3x5o5/4*b - (contains cid) o5/2o3o5x5/4*b - (contains "2doe") ``` otherWythoffians ```x5/2x3/2o5o5*b - [Grünbaumian] x5/2o3/2x5o5*b - (contains cid) x5/2o3/2o5x5*b - (contains "2doe") o5/2x3/2x5o5*b - [Grünbaumian] o5/2x3/2o5x5*b - rawvathi o5/2o3/2x5x5*b - sidipthi x5/2x3/2x5o5*b - [Grünbaumian] x5/2x3/2o5x5*b - [Grünbaumian] x5/2o3/2x5x5*b - gik vipathi o5/2x3/2x5x5*b - [Grünbaumian] x5/2x3/2x5x5*b - [Grünbaumian] ``` ```x5/3x3/2o5o5*b - (contains cid) x5/3o3/2x5o5*b - (contains cid) x5/3o3/2o5x5*b - (contains "2doe") o5/3x3/2x5o5*b - [Grünbaumian] o5/3x3/2o5x5*b - rawvathi o5/3o3/2x5x5*b - sidipthi x5/3x3/2x5o5*b - [Grünbaumian] x5/3x3/2o5x5*b - gapthi x5/3o3/2x5x5*b - o5/3x3/2x5x5*b - [Grünbaumian] x5/3x3/2x5x5*b - [Grünbaumian] ``` ```x5/2x3o5/4o5*b - [Grünbaumian] x5/2o3x5/4o5*b - (contains cid) x5/2o3o5/4x5*b - (contains "2doe") o5/2x3x5/4o5*b - (contains "2gidhei") o5/2x3o5/4x5*b - rawvathi o5/2o3x5/4x5*b - [Grünbaumian] x5/2x3x5/4o5*b - [Grünbaumian] x5/2x3o5/4x5*b - [Grünbaumian] x5/2o3x5/4x5*b - [Grünbaumian] o5/2x3x5/4x5*b - [Grünbaumian] x5/2x3x5/4x5*b - [Grünbaumian] ``` ```x5/2x3o5o5/4*b - [Grünbaumian] x5/2o3x5o5/4*b - (contains cid) x5/2o3o5x5/4*b - (contains "2doe") o5/2x3x5o5/4*b - (contains "2gidhei") o5/2x3o5x5/4*b - [Grünbaumian] o5/2o3x5x5/4*b - sidipthi x5/2x3x5o5/4*b - [Grünbaumian] x5/2x3o5x5/4*b - [Grünbaumian] x5/2o3x5x5/4*b - o5/2x3x5x5/4*b - [Grünbaumian] x5/2x3x5x5/4*b - [Grünbaumian] ``` (partial)snubs andholosnubs ```... ``` ```... ``` ```... ``` ```... ``` o5/3o3o5o5/4*b (µ=674) o5/3o3o5/4o5*b (µ=886) o5/2o3/2o5/4o5/4*b (µ=1994) o5/3o3/2o5/4o5/4*b (µ=2566) quasiregulars ```x5/3o3o5o5/4*b - gishi+gashi (?) (contains v-cid as verf) o5/3x3o5o5/4*b - (contains cid) o5/3o3x5o5/4*b - (contains cid) o5/3o3o5x5/4*b - (contains "2doe") ``` ```x5/3o3o5/4o5*b - gishi+gashi (?) (contains v-cid as verf) o5/3x3o5/4o5*b - (contains cid) o5/3o3x5/4o5*b - (contains cid) o5/3o3o5/4x5*b - (contains "2doe") ``` ```x5/2o3/2o5/4o5/4*b - gishi+gashi (?) (contains v-cid as verf) o5/2x3/2o5/4o5/4*b - (contains cid) o5/2o3/2x5/4o5/4*b - (contains cid) o5/2o3/2o5/4x5/4*b - (contains "2doe") ``` ```x5/3o3/2o5/4o5/4*b - gishi+gashi (?) (contains v-cid as verf) o5/3x3/2o5/4o5/4*b - (contains cid) o5/3o3/2x5/4o5/4*b - (contains cid) o5/3o3/2o5/4x5/4*b - (contains "2doe") ``` otherWythoffians ```x5/3x3o5o5/4*b - (contains cid) x5/3o3x5o5/4*b - (contains cid) x5/3o3o5x5/4*b - (contains "2doe") o5/3x3x5o5/4*b - (contains "2gidhei") o5/3x3o5x5/4*b - [Grünbaumian] o5/3o3x5x5/4*b - sidipthi x5/3x3x5o5/4*b - (contains "2gidhei") x5/3x3o5x5/4*b - [Grünbaumian] x5/3o3x5x5/4*b - gik vipathi o5/3x3x5x5/4*b - [Grünbaumian] x5/3x3x5x5/4*b - [Grünbaumian] ``` ```x5/3x3o5/4o5*b - (contains cid) x5/3o3x5/4o5*b - (contains cid) x5/3o3o5/4x5*b - (contains "2doe") o5/3x3x5/4o5*b - (contains "2gidhei") o5/3x3o5/4x5*b - rawvathi o5/3o3x5/4x5*b - [Grünbaumian] x5/3x3x5/4o5*b - (contains "2gidhei") x5/3x3o5/4x5*b - gapthi x5/3o3x5/4x5*b - [Grünbaumian] o5/3x3x5/4x5*b - [Grünbaumian] x5/3x3x5/4x5*b - [Grünbaumian] ``` ```x5/2x3/2o5/4o5/4*b - [Grünbaumian] x5/2o3/2x5/4o5/4*b - (contains cid) x5/2o3/2o5/4x5/4*b - (contains "2doe") o5/2x3/2x5/4o5/4*b - [Grünbaumian] o5/2x3/2o5/4x5/4*b - [Grünbaumian] o5/2o3/2x5/4x5/4*b - [Grünbaumian] x5/2x3/2x5/4o5/4*b - [Grünbaumian] x5/2x3/2o5/4x5/4*b - [Grünbaumian] x5/2o3/2x5/4x5/4*b - [Grünbaumian] o5/2x3/2x5/4x5/4*b - [Grünbaumian] x5/2x3/2x5/4x5/4*b - [Grünbaumian] ``` ```x5/3x3/2o5/4o5/4*b - (contains cid) x5/3o3/2x5/4o5/4*b - (contains cid) x5/3o3/2o5/4x5/4*b - (contains "2doe") o5/3x3/2x5/4o5/4*b - [Grünbaumian] o5/3x3/2o5/4x5/4*b - [Grünbaumian] o5/3o3/2x5/4x5/4*b - [Grünbaumian] x5/3x3/2x5/4o5/4*b - [Grünbaumian] x5/3x3/2o5/4x5/4*b - [Grünbaumian] x5/3o3/2x5/4x5/4*b - [Grünbaumian] o5/3x3/2x5/4x5/4*b - [Grünbaumian] x5/3x3/2x5/4x5/4*b - [Grünbaumian] ``` (partial)snubs andholosnubs ```... ``` ```... ``` ```... ``` ```... ```

### Hecatonicosachoral ("hyic") Symmetries – type o5o5/2o3/2o5/2*b   (up)

 o5o5/2o3/2o5/2*b (µ=152) o5o5/2o3o5/3*b (µ=208) o5o5/3o3/2o5/3*b (µ=872) quasiregulars ```x5o5/2o3/2o5/2*b - 2gaghi (?) (contains f-"2gissid" as verf) o5x5/2o3/2o5/2*b - (contains "2gissid") o5o5/2x3/2o5/2*b - (contains gacid) ``` ```x5o5/2o3o5/3*b - 2gaghi (?) (contains f-"2gissid" as verf) o5x5/2o3o5/3*b - (contains "2gissid") o5o5/2x3o5/3*b - (contains gacid) o5o5/2o3x5/3*b - (contains gacid) ``` ```x5o5/3o3/2o5/3*b - 2gaghi (?) (contains f-"2gissid" as verf) o5x5/3o3/2o5/3*b - (contains "2gissid") o5o5/3x3/2o5/3*b - (contains gacid) ``` otherWythoffians ```x5x5/2o3/2o5/2*b - (contains "2gissid") x5o5/2x3/2o5/2*b - (contains gacid) o5x5/2x3/2o5/2*b - [Grünbaumian] o5o5/2x3/2x5/2*b - [Grünbaumian] x5x5/2x3/2o5/2*b - [Grünbaumian] x5o5/2x3/2x5/2*b - [Grünbaumian] o5x5/2x3/2x5/2*b - [Grünbaumian] x5x5/2x3/2x5/2*b - [Grünbaumian] ``` ```x5x5/2o3o5/3*b - (contains "2gissid") x5o5/2x3o5/3*b - (contains gacid) x5o5/2o3x5/3*b - (contains gacid) o5x5/2x3o5/3*b - [Grünbaumian] o5x5/2o3x5/3*b - gwavathi o5o5/2x3x5/3*b - (contains "2sidhei") x5x5/2x3o5/3*b - [Grünbaumian] x5x5/2o3x5/3*b - sipthi x5o5/2x3x5/3*b - o5x5/2x3x5/3*b - [Grünbaumian] x5x5/2x3x5/3*b - [Grünbaumian] ``` ```x5x5/3o3/2o5/3*b - (contains "2gissid") x5o5/3x3/2o5/3*b - (contains gacid) o5x5/3x3/2o5/3*b - gwavathi o5o5/3x3/2x5/3*b - [Grünbaumian] x5x5/3x3/2o5/3*b - sipthi x5o5/3x3/2x5/3*b - [Grünbaumian] o5x5/3x3/2x5/3*b - [Grünbaumian] x5x5/3x3/2x5/3*b - [Grünbaumian] ``` (partial)snubs andholosnubs ```... ``` ```... ``` ```... ``` o5/4o5/2o3o5/3*b (µ=992) o5/4o5/2o3/2o5/2*b (µ=1528) o5/4o5/3o3/2o5/3*b (µ=2248) quasiregulars ```x5/4o5/2o3o5/3*b - 2gaghi (?) (contains f-"2gissid" as verf) o5/4x5/2o3o5/3*b - (contains "2gissid") o5/4o5/2x3o5/3*b - (contains gacid) o5/4o5/2o3x5/3*b - (contains gacid) ``` ```x5/4o5/2o3/2o5/2*b - 2gaghi (?) (contains f-"2gissid" as verf) o5/4x5/2o3/2o5/2*b - (contains "2gissid") o5/4o5/2x3/2o5/2*b - (contains gacid) ``` ```x5/4o5/3o3/2o5/3*b - 2gaghi (?) (contains f-"2gissid" as verf) o5/4x5/3o3/2o5/3*b - (contains "2gissid") o5/4o5/3x3/2o5/3*b - (contains gacid) ``` otherWythoffians ```x5/4x5/2o3o5/3*b - [Grünbaumian] x5/4o5/2x3o5/3*b - (contains gacid) x5/4o5/2o3x5/3*b - (contains gacid) o5/4x5/2x3o5/3*b - [Grünbaumian] o5/4x5/2o3x5/3*b - gwavathi o5/4o5/2x3x5/3*b - (contains "2sidhei") x5/4x5/2x3o5/3*b - [Grünbaumian] x5/4x5/2o3x5/3*b - [Grünbaumian] x5/4o5/2x3x5/3*b - o5/4x5/2x3x5/3*b - [Grünbaumian] x5/4x5/2x3x5/3*b - [Grünbaumian] ``` ```x5/4x5/2o3/2o5/2*b - [Grünbaumian] x5/4o5/2x3/2o5/2*b - (contains gacid) o5/4x5/2x3/2o5/2*b - [Grünbaumian] o5/4o5/2x3/2x5/2*b - [Grünbaumian] x5/4x5/2x3/2o5/2*b - [Grünbaumian] x5/4o5/2x3/2x5/2*b - [Grünbaumian] o5/4x5/2x3/2x5/2*b - [Grünbaumian] x5/4x5/2x3/2x5/2*b - [Grünbaumian] ``` ```x5/4x5/3o3/2o5/3*b - [Grünbaumian] x5/4o5/3x3/2o5/3*b - (contains gacid) o5/4x5/3x3/2o5/3*b - gwavathi o5/4o5/3x3/2x5/3*b - [Grünbaumian] x5/4x5/3x3/2o5/3*b - [Grünbaumian] x5/4o5/3x3/2x5/3*b - [Grünbaumian] o5/4x5/3x3/2x5/3*b - [Grünbaumian] x5/4x5/3x3/2x5/3*b - [Grünbaumian] ``` (partial)snubs andholosnubs ```... ``` ```... ``` ```... ```

### Hecatonicosachoral ("hyic") Symmetries – type o5/2o5o3/2o5*b   (up)

 o5/2o5o3/2o5*b (µ=8) o5/3o5o3/2o5*b (µ=232) o5/2o5o3o5/4*b (µ=352) quasiregulars ```x5/2o5o3/2o5*b - 2sishi (?) (contains v-"2doe" as verf) o5/2x5o3/2o5*b - (contains "2doe") o5/2o5x3/2o5*b - (contains cid) ``` ```x5/3o5o3/2o5*b - 2sishi (?) (contains v-"2doe" as verf) o5/3x5o3/2o5*b - (contains "2doe") o5/3o5x3/2o5*b - (contains cid) ``` ```x5/2o5o3o5/4*b - 2sishi (?) (contains v-"2doe" as verf) o5/2x5o3o5/4*b - (contains "2doe") o5/2o5x3o5/4*b - (contains cid) o5/2o5o3x5/4*b - (contains cid) ``` otherWythoffians ```x5/2x5o3/2o5*b - [Grünbaumian] x5/2o5x3/2o5*b - (contains cid) o5/2x5x3/2o5*b - srawvathi o5/2o5x3/2x5*b - [Grünbaumian] x5/2x5x3/2o5*b - [Grünbaumian] x5/2o5x3/2x5*b - [Grünbaumian] o5/2x5x3/2x5*b - [Grünbaumian] x5/2x5x3/2x5*b - [Grünbaumian] ``` ```x5/3x5o3/2o5*b - (contains "2doe") x5/3o5x3/2o5*b - (contains cid) o5/3x5x3/2o5*b - srawvathi o5/3o5x3/2x5*b - [Grünbaumian] x5/3x5x3/2o5*b - gipthi x5/3o5x3/2x5*b - [Grünbaumian] o5/3x5x3/2x5*b - [Grünbaumian] x5/3x5x3/2x5*b - [Grünbaumian] ``` ```x5/2x5o3o5/4*b - [Grünbaumian] x5/2o5x3o5/4*b - (contains cid) x5/2o5o3x5/4*b - (contains cid) o5/2x5x3o5/4*b - srawvathi o5/2x5o3x5/4*b - [Grünbaumian] o5/2o5x3x5/4*b - (contains "2gidhei") x5/2x5x3o5/4*b - [Grünbaumian] x5/2x5o3x5/4*b - [Grünbaumian] x5/2o5x3x5/4*b - o5/2x5x3x5/4*b - [Grünbaumian] x5/2x5x3x5/4*b - [Grünbaumian] ``` (partial)snubs andholosnubs ```... ``` ```... ``` ```... ``` o5/3o5o3o5/4*b (µ=848) o5/2o5/4o3/2o5/4*b (µ=2168) o5/3o5/4o3/2o5/4*b (µ=2392) quasiregulars ```x5/3o5o3o5/4*b - 2sishi (?) (contains v-"2doe" as verf) o5/3x5o3o5/4*b - (contains "2doe") o5/3o5x3o5/4*b - (contains cid) o5/3o5o3x5/4*b - (contains cid) ``` ```x5/2o5/4o3/2o5/4*b - 2sishi (?) (contains v-"2doe" as verf) o5/2x5/4o3/2o5/4*b - (contains "2doe") o5/2o5/4x3/2o5/4*b - (contains cid) ``` ```x5/3o5/4o3/2o5/4*b - 2sishi (?) (contains v-"2doe" as verf) o5/3x5/4o3/2o5/4*b - (contains "2doe") o5/3o5/4x3/2o5/4*b - (contains cid) ``` otherWythoffians ```x5/3x5o3o5/4*b - (contains "2doe") x5/3o5x3o5/4*b - (contains cid) x5/3o5o3x5/4*b - (contains cid) o5/3x5x3o5/4*b - srawvathi o5/3x5o3x5/4*b - [Grünbaumian] o5/3o5x3x5/4*b - (contains "2gidhei") x5/3x5x3o5/4*b - gipthi x5/3x5o3x5/4*b - [Grünbaumian] x5/3o5x3x5/4*b - o5/3x5x3x5/4*b - [Grünbaumian] x5/3x5x3x5/4*b - [Grünbaumian] ``` ```x5/2x5/4o3/2o5/4*b - [Grünbaumian] x5/2o5/4x3/2o5/4*b - (contains cid) o5/2x5/4x3/2o5/4*b - [Grünbaumian] o5/2o5/4x3/2x5/4*b - [Grünbaumian] x5/2x5/4x3/2o5/4*b - [Grünbaumian] x5/2o5/4x3/2x5/4*b - [Grünbaumian] o5/2x5/4x3/2x5/4*b - [Grünbaumian] x5/2x5/4x3/2x5/4*b - [Grünbaumian] ``` ```x5/3x5/4o3/2o5/4*b - (contains "2doe") x5/3o5/4x3/2o5/4*b - (contains cid) o5/3x5/4x3/2o5/4*b - [Grünbaumian] o5/3o5/4x3/2x5/4*b - [Grünbaumian] x5/3x5/4x3/2o5/4*b - [Grünbaumian] x5/3o5/4x3/2x5/4*b - [Grünbaumian] o5/3x5/4x3/2x5/4*b - [Grünbaumian] x5/3x5/4x3/2x5/4*b - [Grünbaumian] ``` (partial)snubs andholosnubs ```... ``` ```... ``` ```... ```

### Hecatonicosachoral ("hyic") Symmetries – type o5o5/2o5/2o5/2*b   (up)

 o5o5/2o5/2o5/2*b (µ=12) o5o5/2o5/3o5/3*b (µ=348) o5/4o5/2o5/2o5/2*b (µ=708) quasiregulars ```x5o5/2o5/2o5/2*b - 2gohi (?) (contains f-"2sissid" as verf) o5x5/2o5/2o5/2*b - (contains "2sissid") o5o5/2x5/2o5/2*b - (contains "2sissid") ``` ```x5o5/2o5/3o5/3*b - 2gohi (?) (contains f-"2sissid" as verf) o5x5/2o5/3o5/3*b - (contains "2sissid") o5o5/2x5/3o5/3*b - (contains "2sissid") o5o5/2o5/3x5/3*b - (contains "2sissid") ``` ```x5/4o5/2o5/2o5/2*b - 2gohi (?) (contains f-"2sissid" as verf) o5/4x5/2o5/2o5/2*b - (contains "2sissid") o5/4o5/2x5/2o5/2*b - (contains "2sissid") ``` otherWythoffians ```x5x5/2o5/2o5/2*b - (contains "2sissid") x5o5/2x5/2o5/2*b - (contains "2sissid") o5x5/2x5/2o5/2*b - [Grünbaumian] o5o5/2x5/2x5/2*b - [Grünbaumian] x5x5/2x5/2o5/2*b - [Grünbaumian] x5o5/2x5/2x5/2*b - [Grünbaumian] o5x5/2x5/2x5/2*b - [Grünbaumian] x5x5/2x5/2x5/2*b - [Grünbaumian] ``` ```x5x5/2o5/3o5/3*b - (contains "2sissid") x5o5/2x5/3o5/3*b - (contains "2sissid") x5o5/2o5/3x5/3*b - (contains "2sissid") o5x5/2x5/3o5/3*b - [Grünbaumian] o5x5/2o5/3x5/3*b - (contains "2gidhid") o5o5/2x5/3x5/3*b - (contains "2gidhid") x5x5/2x5/3o5/3*b - [Grünbaumian] x5x5/2o5/3x5/3*b - (contains "2gidhid") x5o5/2x5/3x5/3*b - o5x5/2x5/3x5/3*b - [Grünbaumian] x5x5/2x5/3x5/3*b - [Grünbaumian] ``` ```x5/4x5/2o5/2o5/2*b - [Grünbaumian] x5/4o5/2x5/2o5/2*b - (contains "2sissid") o5/4x5/2x5/2o5/2*b - [Grünbaumian] o5/4o5/2x5/2x5/2*b - [Grünbaumian] x5/4x5/2x5/2o5/2*b - [Grünbaumian] x5/4o5/2x5/2x5/2*b - [Grünbaumian] o5/4x5/2x5/2x5/2*b - [Grünbaumian] x5/4x5/2x5/2x5/2*b - [Grünbaumian] ``` (partial)snubs andholosnubs ```... ``` ```... ``` ```... ``` o5o5/3o5/2o5/3*b (µ=732) o5/4o5/3o5/2o5/3*b (µ=1428) o5/4o5/2o5/3o5/3*b (µ=1812) quasiregulars ```x5o5/3o5/2o5/3*b - 2gohi (?) (contains f-"2sissid" as verf) o5x5/3o5/2o5/3*b - (contains "2sissid") o5o5/3x5/2o5/3*b - (contains "2sissid") ``` ```x5/4o5/3o5/2o5/3*b - 2gohi (?) (contains f-"2sissid" as verf) o5/4x5/3o5/2o5/3*b - (contains "2sissid") o5/4o5/3x5/2o5/3*b - (contains "2sissid") ``` ```x5/4o5/2o5/3o5/3*b - 2gohi (?) (contains f-"2sissid" as verf) o5/4x5/2o5/3o5/3*b - (contains "2sissid") o5/4o5/2x5/3o5/3*b - (contains "2sissid") o5/4o5/2o5/3x5/3*b - (contains "2sissid") ``` otherWythoffians ```x5x5/3o5/2o5/3*b - (contains "2sissid") x5o5/3x5/2o5/3*b - (contains "2sissid") o5x5/3x5/2o5/3*b - (contains "2gidhid") o5o5/3x5/2x5/3*b - [Grünbaumian] x5x5/3x5/2o5/3*b - (contains "2gidhid") x5o5/3x5/2x5/3*b - [Grünbaumian] o5x5/3x5/2x5/3*b - [Grünbaumian] x5x5/3x5/2x5/3*b - [Grünbaumian] ``` ```x5/4x5/3o5/2o5/3*b - [Grünbaumian] x5/4o5/3x5/2o5/3*b - (contains "2sissid") o5/4x5/3x5/2o5/3*b - (contains "2gidhid") o5/4o5/3x5/2x5/3*b - [Grünbaumian] x5/4x5/3x5/2o5/3*b - [Grünbaumian] x5/4o5/3x5/2x5/3*b - [Grünbaumian] o5/4x5/3x5/2x5/3*b - [Grünbaumian] x5/4x5/3x5/2x5/3*b - [Grünbaumian] ``` ```x5/4x5/2o5/3o5/3*b - [Grünbaumian] x5/4o5/2x5/3o5/3*b - (contains "2sissid") x5/4o5/2o5/3x5/3*b - (contains "2sissid") o5/4x5/2x5/3o5/3*b - [Grünbaumian] o5/4x5/2o5/3x5/3*b - (contains "2gidhid") o5/4o5/2x5/3x5/3*b - (contains "2gidhid") x5/4x5/2x5/3o5/3*b - [Grünbaumian] x5/4x5/2o5/3x5/3*b - [Grünbaumian] x5/4o5/2x5/3x5/3*b - o5/4x5/2x5/3x5/3*b - [Grünbaumian] x5/4x5/2x5/3x5/3*b - [Grünbaumian] ``` (partial)snubs andholosnubs ```... ``` ```... ``` ```... ```

### Hecatonicosachoral ("hyic") Symmetries – type o5/2o5o5/4o5*b   (up)

 o5/2o5o5/4o5*b (µ=132) o5/2o5o5o5/4*b (µ=228) o5/3o5o5o5/4*b (µ=492) quasiregulars ```x5/2o5o5/4o5*b - 2gashi (?) (contains v-"2gad" as verf) o5/2x5o5/4o5*b - (contains "2gad") o5/2o5x5/4o5*b - (contains "2gad") ``` ```x5/2o5o5o5/4*b - 2gashi (?) (contains v-"2gad" as verf) o5/2x5o5o5/4*b - (contains "2gad") o5/2o5x5o5/4*b - (contains "2gad") o5/2o5o5x5/4*b - (contains "2gad") ``` ```x5/3o5o5o5/4*b - 2gashi (?) (contains v-"2gad" as verf) o5/3x5o5o5/4*b - (contains "2gad") o5/3o5x5o5/4*b - (contains "2gad") o5/3o5o5x5/4*b - (contains "2gad") ``` otherWythoffians ```x5/2x5o5/4o5*b - [Grünbaumian] x5/2o5x5/4o5*b - (contains "2gad") o5/2x5x5/4o5*b - (contains "2sidhid") o5/2o5x5/4x5*b - [Grünbaumian] x5/2x5x5/4o5*b - [Grünbaumian] x5/2o5x5/4x5*b - [Grünbaumian] o5/2x5x5/4x5*b - [Grünbaumian] x5/2x5x5/4x5*b - [Grünbaumian] ``` ```x5/2x5o5o5/4*b - [Grünbaumian] x5/2o5x5o5/4*b - (contains "2gad") x5/2o5o5x5/4*b - (contains "2gad") o5/2x5x5o5/4*b - (contains "2sidhid") o5/2x5o5x5/4*b - [Grünbaumian] o5/2o5x5x5/4*b - (contains "2sidhid") x5/2x5x5o5/4*b - [Grünbaumian] x5/2x5o5x5/4*b - [Grünbaumian] x5/2o5x5x5/4*b - o5/2x5x5x5/4*b - [Grünbaumian] x5/2x5x5x5/4*b - [Grünbaumian] ``` ```x5/3x5o5o5/4*b - (contains "2gad") x5/3o5x5o5/4*b - (contains "2gad") x5/3o5o5x5/4*b - (contains "2gad") o5/3x5x5o5/4*b - (contains "2sidhid") o5/3x5o5x5/4*b - [Grünbaumian] o5/3o5x5x5/4*b - (contains "2sidhid") x5/3x5x5o5/4*b - (contains "2sidhid") x5/3x5o5x5/4*b - [Grünbaumian] x5/3o5x5x5/4*b - o5/3x5x5x5/4*b - [Grünbaumian] x5/3x5x5x5/4*b - [Grünbaumian] ``` (partial)snubs andholosnubs ```... ``` ```... ``` ```... ``` o5/3o5o5/4o5*b (µ=588) o5/2o5/4o5/4o5/4*b (µ=2292) o5/3o5/4o5/4o5/4*b (µ=2748) quasiregulars ```x5/3o5o5/4o5*b - 2gashi (?) (contains v-"2gad" as verf) o5/3x5o5/4o5*b - (contains "2gad") o5/3o5x5/4o5*b - (contains "2gad") ``` ```x5/2o5/4o5/4o5/4*b - 2gashi (?) (contains v-"2gad" as verf) o5/2x5/4o5/4o5/4*b - (contains "2gad") o5/2o5/4x5/4o5/4*b - (contains "2gad") ``` ```x5/3o5/4o5/4o5/4*b - 2gashi (?) (contains v-"2gad" as verf) o5/3x5/4o5/4o5/4*b - (contains "2gad") o5/3o5/4x5/4o5/4*b - (contains "2gad") ``` otherWythoffians ```x5/3x5o5/4o5*b - (contains "2gad") x5/3o5x5/4o5*b - (contains "2gad") o5/3x5x5/4o5*b - (contains "2sidhid") o5/3o5x5/4x5*b - [Grünbaumian] x5/3x5x5/4o5*b - (contains "2sidhid") x5/3o5x5/4x5*b - [Grünbaumian] o5/3x5x5/4x5*b - [Grünbaumian] x5/3x5x5/4x5*b - [Grünbaumian] ``` ```x5/2x5/4o5/4o5/4*b - [Grünbaumian] x5/2o5/4x5/4o5/4*b - (contains "2gad") o5/2x5/4x5/4o5/4*b - [Grünbaumian] o5/2o5/4x5/4x5/4*b - [Grünbaumian] x5/2x5/4x5/4o5/4*b - [Grünbaumian] x5/2o5/4x5/4x5/4*b - [Grünbaumian] o5/2x5/4x5/4x5/4*b - [Grünbaumian] x5/2x5/4x5/4x5/4*b - [Grünbaumian] ``` ```x5/3x5/4o5/4o5/4*b - (contains "2gad") x5/3o5/4x5/4o5/4*b - (contains "2gad") o5/3x5/4x5/4o5/4*b - [Grünbaumian] o5/3o5/4x5/4x5/4*b - [Grünbaumian] x5/3x5/4x5/4o5/4*b - [Grünbaumian] x5/3o5/4x5/4x5/4*b - [Grünbaumian] o5/3x5/4x5/4x5/4*b - [Grünbaumian] x5/3x5/4x5/4x5/4*b - [Grünbaumian] ``` (partial)snubs andholosnubs ```... ``` ```... ``` ```... ```

 loop ones ```o-P-o-Q-o-R-o-S-*a = o---P---o | | S Q | | o---R---o ```

### Tesseractic ("tessic") Symmetries   (up)

 o3o3o3o3/2*a (µ=8) o3o3/2o3/2o3/2*a (µ=40) quasiregulars ```x3o3o3o3/2*a - 2tho (?) o3x3o3o3/2*a - 2tho (?) ``` ```x3o3/2o3/2o3/2*a - 2tho (?) o3o3/2x3/2o3/2*a - 2tho (?) ``` otherWythoffians ```x3x3o3o3/2*a - 2firt (?) x3o3x3o3/2*a - (contains "2thah") x3o3o3x3/2*a - [Grünbaumian] o3x3x3o3/2*a - 2firt (?) x3x3x3o3/2*a - (contains "2thah") x3x3o3x3/2*a - [Grünbaumian] x3x3x3x3/2*a - [Grünbaumian] ``` ```x3x3/2o3/2o3/2*a - 2firt (?) x3o3/2x3/2o3/2*a - (contains "2thah") x3o3/2o3/2x3/2*a - [Grünbaumian] o3o3/2x3/2x3/2*a - [Grünbaumian] x3x3/2x3/2o3/2*a - [Grünbaumian] x3o3/2x3/2x3/2*a - [Grünbaumian] x3x3/2x3/2x3/2*a - [Grünbaumian] ``` (partial)snubs andholosnubs ```... ``` ```... ```

### Icositetrachoral ("icoic") Symmetries   (up)

 o3o4o3/2o4*a (µ=10) o3o4o3o4/3*a (µ=14) o3/2o4o3/2o4/3*a (µ=110) o3o4/3o3/2o4/3*a (µ=154) quasiregulars ```x3o4o3/2o4*a - ico+gico+24co (?) o3o4x3/2o4*a - ico+gico+24co (?) ``` ```x3o4o3o4/3*a - ico+gico+24co (?) o3x4o3o4/3*a - ico+gico+24co (?) ``` ```x3/2o4o3/2o4/3*a - ico+gico+24co (?) o3/2x4o3/2o4/3*a - ico+gico+24co (?) ``` ```x3o4/3o3/2o4/3*a - ico+gico+24co (?) o3o4/3x3/2o4/3*a - ico+gico+24co (?) ``` otherWythoffians ```x3x4o3/2o4*a - 2frico (?) x3o4x3/2o4*a - rafficdi x3o4o3/2x4*a - siddic o3o4x3/2x4*a - [Grünbaumian] x3x4x3/2o4*a - guti x3o4x3/2x4*a - [Grünbaumian] x3x4x3/2x4*a - [Grünbaumian] ``` ```x3x4o3o4/3*a - 2frico (?) x3o4x3o4/3*a - rafficdi x3o4o3x4/3*a - giddic o3x4x3o4/3*a - siddic x3x4x3o4/3*a - guti x3x4o3x4/3*a - suti x3x4x3x4/3*a - doc ``` ```x3/2x4o3/2o4/3*a - [Grünbaumian] x3/2o4x3/2o4/3*a - rafficdi x3/2o4o3/2x4/3*a - giddic o3/2x4x3/2o4/3*a - siddic x3/2x4x3/2o4/3*a - [Grünbaumian] x3/2x4o3/2x4/3*a - [Grünbaumian] x3/2x4x3/2x4/3*a - [Grünbaumian] ``` ```x3x4/3o3/2o4/3*a - 2frico (?) x3o4/3x3/2o4/3*a - rafficdi x3o4/3o3/2x4/3*a - giddic o3o4/3x3/2x4/3*a - [Grünbaumian] x3x4/3x3/2o4/3*a - suti x3o4/3x3/2x4/3*a - [Grünbaumian] x3x4/3x3/2x4/3*a - [Grünbaumian] ``` (partial)snubs andholosnubs ```... ``` ```... ``` ```... ``` ```... ```

### Hecatonicosachoral ("hyic") Symmetries – type o3o3/2o3o5*a   (up)

 o3o3/2o3o5*a (µ=14) o3o3o3/2o5*a (µ=106) o3o3o3o5/4*a (µ=494) quasiregulars ```x3o3/2o3o5*a - sirdtaxady o3x3/2o3o5*a - gidtixhi+dox (?) ``` ```x3o3o3/2o5*a - sirdtaxady o3x3o3/2o5*a - gidtixhi+dox (?) o3o3x3/2o5*a - gidtixhi+dox (?) o3o3o3/2x5*a - sirdtaxady ``` ```x3o3o3o5/4*a - sirdtaxady o3x3o3o5/4*a - gidtixhi+dox (?) ``` otherWythoffians ```x3x3/2o3o5*a - gadixady x3o3/2x3o5*a - (contains "2thah") x3o3/2o3x5*a - 2fry (?) o3x3/2x3o5*a - [Grünbaumian] x3x3/2x3o5*a - [Grünbaumian] x3x3/2o3x5*a - (contains "2thah") x3x3/2x3x5*a - [Grünbaumian] ``` ```x3x3o3/2o5*a - gadixady x3o3x3/2o5*a - (contains gicdatrid) x3o3o3/2x5*a - 2fry (?) o3x3x3/2o5*a - 2prapvixhi (?) o3x3o3/2x5*a - (contains "2thah") o3o3x3/2x5*a - [Grünbaumian] x3x3x3/2o5*a - (contains gicdatrid) x3x3o3/2x5*a - (contains "2thah") x3o3x3/2x5*a - [Grünbaumian] o3x3x3/2x5*a - [Grünbaumian] x3x3x3/2x5*a - [Grünbaumian] ``` ```x3x3o3o5/4*a - gadixady x3o3x3o5/4*a - (contains gicdatrid) x3o3o3x5/4*a - [Grünbaumian] o3x3x3o5/4*a - 2prapvixhi (?) x3x3x3o5/4*a - (contains gicdatrid) x3x3o3x5/4*a - [Grünbaumian] x3x3x3x5/4*a - [Grünbaumian] ``` (partial)snubs andholosnubs ```... ``` ```... ``` ```... ``` o3/2o3/2o3/2o5*a (µ=1214) o3/2o3o3/2o5/4*a (µ=1694) o3o3/2o3/2o5/4*a (µ=1786) quasiregulars ```x3/2o3/2o3/2o5*a - sirdtaxady o3/2x3/2o3/2o5*a - gidtixhi+dox (?) ``` ```x3/2o3o3/2o5/4*a - sirdtaxady o3/2x3o3/2o5/4*a - gidtixhi+dox (?) ``` ```x3o3/2o3/2o5/4*a - sirdtaxady o3x3/2o3/2o5/4*a - gidtixhi+dox (?) o3o3/2x3/2o5/4*a - gidtixhi+dox (?) o3o3/2o3/2x5/4*a - sirdtaxady ``` otherWythoffians ```x3/2x3/2o3/2o5*a - [Grünbaumian] x3/2o3/2x3/2o5*a - (contains gicdatrid) x3/2o3/2o3/2x5*a - 2fry (?) o3/2x3/2x3/2o5*a - [Grünbaumian] x3/2x3/2x3/2o5*a - [Grünbaumian] x3/2x3/2o3/2x5*a - [Grünbaumian] x3/2x3/2x3/2x5*a - [Grünbaumian] ``` ```x3/2x3o3/2o5/4*a - [Grünbaumian] x3/2o3x3/2o5/4*a - (contains "2thah") x3/2o3o3/2x5/4*a - [Grünbaumian] o3/2x3x3/2o5/4*a - 2prapvixhi (?) x3/2x3x3/2o5/4*a - [Grünbaumian] x3/2x3o3/2x5/4*a - [Grünbaumian] x3/2x3x3/2x5/4*a - [Grünbaumian] ``` ```x3x3/2o3/2o5/4*a - gadixady x3o3/2x3/2o5/4*a - (contains "2thah") x3o3/2o3/2x5/4*a - [Grünbaumian] o3x3/2x3/2o5/4*a - [Grünbaumian] o3x3/2o3/2x5/4*a - (contains gicdatrid) o3o3/2x3/2x5/4*a - [Grünbaumian] x3x3/2x3/2o5/4*a - [Grünbaumian] x3x3/2o3/2x5/4*a - [Grünbaumian] x3o3/2x3/2x5/4*a - [Grünbaumian] o3x3/2x3/2x5/4*a - [Grünbaumian] x3x3/2x3/2x5/4*a - [Grünbaumian] ``` (partial)snubs andholosnubs ```... ``` ```... ``` ```... ```

### Hecatonicosachoral ("hyic") Symmetries – type o3o3o3o5/2*a   (up)

 o3o3o3o5/2*a (µ=34) o3o3o3/2o5/3*a (µ=566) o3o3/2o3/2o5/2*a (µ=806) quasiregulars ```x3o3o3o5/2*a - gadtaxady o3x3o3o5/2*a - sidtixhi+dox (?) ``` ```x3o3o3/2o5/3*a - gadtaxady o3x3o3/2o5/3*a - sidtixhi+dox (?) o3o3x3/2o5/3*a - sidtixhi+dox (?) o3o3o3/2x5/3*a - gadtaxady ``` ```x3o3/2o3/2o5/2*a - gadtaxady o3x3/2o3/2o5/2*a - sidtixhi+dox (?) o3o3/2x3/2o5/2*a - sidtixhi+dox (?) o3o3/2o3/2x5/2*a - gadtaxady ``` otherWythoffians ```x3x3o3o5/2*a - sadixady x3o3x3o5/2*a - (contains sicdatrid) x3o3o3x5/2*a - [Grünbaumian] o3x3x3o5/2*a - 2papvixhi (?) x3x3x3o5/2*a - (contains sicdatrid) x3x3o3x5/2*a - [Grünbaumian] x3x3x3x5/2*a - [Grünbaumian] ``` ```x3x3o3/2o5/3*a - sadixady x3o3x3/2o5/3*a - (contains sicdatrid) x3o3o3/2x5/3*a - 2firgogishi (?) o3x3x3/2o5/3*a - 2papvixhi (?) o3x3o3/2x5/3*a - (contains "2thah") o3o3x3/2x5/3*a - [Grünbaumian] x3x3x3/2o5/3*a - (contains sicdatrid) x3x3o3/2x5/3*a - (contains "2thah") x3o3x3/2x5/3*a - [Grünbaumian] o3x3x3/2x5/3*a - [Grünbaumian] x3x3x3/2x5/3*a - [Grünbaumian] ``` ```x3x3/2o3/2o5/2*a - sadixady x3o3/2x3/2o5/2*a - (contains "2thah") x3o3/2o3/2x5/2*a - [Grünbaumian] o3x3/2x3/2o5/2*a - [Grünbaumian] o3x3/2o3/2x5/2*a - (contains sicdatrid) o3o3/2x3/2x5/2*a - [Grünbaumian] x3x3/2x3/2o5/2*a - [Grünbaumian] x3x3/2o3/2x5/2*a - [Grünbaumian] x3o3/2x3/2x5/2*a - [Grünbaumian] o3x3/2x3/2x5/2*a - [Grünbaumian] x3x3/2x3/2x5/2*a - [Grünbaumian] ``` (partial)snubs andholosnubs ```... ``` ```... ``` ```... ``` o3o3/2o3o5/3*a (µ=994) o3/2o3o3/2o5/2*a (µ=1254) o3/2o3/2o3/2o5/3*a (µ=2194) quasiregulars ```x3o3/2o3o5/3*a - gadtaxady o3x3/2o3o5/3*a - sidtixhi+dox (?) ``` ```x3/2o3o3/2o5/2*a - gadtaxady o3/2x3o3/2o5/2*a - sidtixhi+dox (?) ``` ```x3/2o3/2o3/2o5/3*a - gadtaxady o3/2x3/2o3/2o5/3*a - sidtixhi+dox (?) ``` otherWythoffians ```x3x3/2o3o5/3*a - sadixady x3o3/2x3o5/3*a - (contains "2thah") x3o3/2o3x5/3*a - 2firgogishi (?) o3x3/2x3o5/3*a - [Grünbaumian] x3x3/2x3o5/3*a - [Grünbaumian] x3x3/2o3x5/3*a - (contains "2thah") x3x3/2x3x5/3*a - [Grünbaumian] ``` ```x3/2x3o3/2o5/2*a - [Grünbaumian] x3/2o3x3/2o5/2*a - (contains "2thah") x3/2o3o3/2x5/2*a - [Grünbaumian] o3/2x3x3/2o5/2*a - 2papvixhi (?) x3/2x3x3/2o5/2*a - [Grünbaumian] x3/2x3o3/2x5/2*a - [Grünbaumian] x3/2x3x3/2x5/2*a - [Grünbaumian] ``` ```x3/2x3/2o3/2o5/3*a - [Grünbaumian] x3/2o3/2x3/2o5/3*a - (contains sicdatrid) x3/2o3/2o3/2x5/3*a - 2firgogishi (?) o3/2x3/2x3/2o5/3*a - [Grünbaumian] x3/2x3/2x3/2o5/3*a - [Grünbaumian] x3/2x3/2o3/2x5/3*a - [Grünbaumian] x3/2x3/2x3/2x5/3*a - [Grünbaumian] ``` (partial)snubs andholosnubs ```... ``` ```... ``` ```... ```

### Hecatonicosachoral ("hyic") Symmetries – type o3o5o3/2o5*a   (up)

 o3o5o3/2o5*a (µ=44) o3o5o3o5/4*a (µ=76) o3/2o5o3/2o5/4*a (µ=1276) o3o5/4o3/2o5/4*a (µ=2204) quasiregulars ```x3o5o3/2o5*a - fix+gahi+120id (?) o3o5x3/2o5*a - fix+gahi+120id (?) ``` ```x3o5o3o5/4*a - fix+gahi+120id (?) o3x5o3o5/4*a - fix+gahi+120id (?) ``` ```x3/2o5o3/2o5/4*a - fix+gahi+120id (?) o3/2x5o3/2o5/4*a - fix+gahi+120id (?) ``` ```x3o5/4o3/2o5/4*a - fix+gahi+120id (?) o3o5/4x3/2o5/4*a - fix+gahi+120id (?) ``` otherWythoffians ```x3x5o3/2o5*a - 2firsashi (?) x3o5x3/2o5*a - (contains gicdatrid) x3o5o3/2x5*a - 2sprapivady (?) o3o5x3/2x5*a - [Grünbaumian] x3x5x3/2o5*a - (contains gicdatrid) x3o5x3/2x5*a - [Grünbaumian] x3x5x3/2x5*a - [Grünbaumian] ``` ```x3x5o3o5/4*a - 2firsashi (?) x3o5x3o5/4*a - (contains gicdatrid) x3o5o3x5/4*a - [Grünbaumian] o3x5x3o5/4*a - 2sprapivady (?) x3x5x3o5/4*a - (contains gicdatrid) x3x5o3x5/4*a - [Grünbaumian] x3x5x3x5/4*a - [Grünbaumian] ``` ```x3/2x5o3/2o5/4*a - [Grünbaumian] x3/2o5x3/2o5/4*a - (contains gicdatrid) x3/2o5o3/2x5/4*a - [Grünbaumian] o3/2x5x3/2o5/4*a - 2sprapivady (?) x3/2x5x3/2o5/4*a - [Grünbaumian] x3/2x5o3/2x5/4*a - [Grünbaumian] x3/2x5x3/2x5/4*a - [Grünbaumian] ``` ```x3x5/4o3/2o5/4*a - 2firsashi (?) x3o5/4x3/2o5/4*a - (contains gicdatrid) x3o5/4o3/2x5/4*a - [Grünbaumian] o3o5/4x3/2x5/4*a - [Grünbaumian] x3x5/4x3/2o5/4*a - [Grünbaumian] x3o5/4x3/2x5/4*a - [Grünbaumian] x3x5/4x3/2x5/4*a - [Grünbaumian] ``` (partial)snubs andholosnubs ```... ``` ```... ``` ```... ``` ```... ```

### Hecatonicosachoral ("hyic") Symmetries – type o3o5/2o3o5/3*a   (up)

 o3o5/2o3o5/3*a (µ=364) o3o5/2o3/2o5/2*a (µ=476) o3o5/3o3/2o5/3*a (µ=1196) o3/2o5/2o3/2o5/3*a (µ=1564) quasiregulars ```x3o5/2o3o5/3*a - gofix+gishi+120gid (?) o3x5/2o3o5/3*a - gofix+gishi+120gid (?) ``` ```x3o5/2o3/2o5/2*a - gofix+gishi+120gid (?) o3o5/2x3/2o5/2*a - gofix+gishi+120gid (?) ``` ```x3o5/3o3/2o5/3*a - gofix+gishi+120gid (?) o3o5/3x3/2o5/3*a - gofix+gishi+120gid (?) ``` ```x3/2o5/2o3/2o5/3*a - gofix+gishi+120gid (?) o3/2x5/2o3/2o5/3*a - gofix+gishi+120gid (?) ``` otherWythoffians ```x3x5/2o3o5/3*a - 2firgaghi (?) x3o5/2x3o5/3*a - (contains sicdatrid) x3o5/2o3x5/3*a - 2gippapivady (?) o3x5/2x3o5/3*a - [Grünbaumian] x3x5/2x3o5/3*a - [Grünbaumian] x3x5/2o3x5/3*a - (contains sicdatrid) x3x5/2x3x5/3*a - [Grünbaumian] ``` ```x3x5/2o3/2o5/2*a - 2firgaghi (?) x3o5/2x3/2o5/2*a - (contains sicdatrid) x3o5/2o3/2x5/2*a - [Grünbaumian] o3o5/2x3/2x5/2*a - [Grünbaumian] x3x5/2x3/2o5/2*a - [Grünbaumian] x3o5/2x3/2x5/2*a - [Grünbaumian] x3x5/2x3/2x5/2*a - [Grünbaumian] ``` ```x3x5/3o3/2o5/3*a - 2firgaghi (?) x3o5/3x3/2o5/3*a - (contains sicdatrid) x3o5/3o3/2x5/3*a - 2gippapivady (?) o3o5/3x3/2x5/3*a - [Grünbaumian] x3x5/3x3/2o5/3*a - (contains sicdatrid) x3o5/3x3/2x5/3*a - [Grünbaumian] x3x5/3x3/2x5/3*a - [Grünbaumian] ``` ```x3/2x5/2o3/2o5/3*a - [Grünbaumian] x3/2o5/2x3/2o5/3*a - (contains sicdatrid) x3/2o5/2o3/2x5/3*a - 2gippapivady (?) o3/2x5/2x3/2o5/3*a - [Grünbaumian] x3/2x5/2x3/2o5/3*a - [Grünbaumian] x3/2x5/2o3/2x5/3*a - [Grünbaumian] x3/2x5/2x3/2x5/3*a - [Grünbaumian] ``` (partial)snubs andholosnubs ```... ``` ```... ``` ```... ``` ```... ```

### Hecatonicosachoral ("hyic") Symmetries – type o3o3o5o5/3*a   (up)

 o3o3o5o5/3*a (µ=55) o3/2o3o5o5/2*a (µ=65) o3o3/2o5o5/2*a (µ=295) o3o3o5/4o5/2*a (µ=545) quasiregulars ```x3o3o5o5/3*a - gax+gashi+120gid (?) o3x3o5o5/3*a - dittady+dox (?) o3o3x5o5/3*a - ex+gohi+120id (?) o3o3o5x5/3*a - radatathi ``` ```x3/2o3o5o5/2*a - gax+gashi+120gid (?) o3/2x3o5o5/2*a - dittady+dox (?) o3/2o3x5o5/2*a - ex+gohi+120id (?) o3/2o3o5x5/2*a - radatathi ``` ```x3o3/2o5o5/2*a - gax+gashi+120gid (?) o3x3/2o5o5/2*a - dittady+dox (?) o3o3/2x5o5/2*a - ex+gohi+120id (?) o3o3/2o5x5/2*a - radatathi ``` ```x3o3o5/4o5/2*a - gax+gashi+120gid (?) o3x3o5/4o5/2*a - dittady+dox (?) o3o3x5/4o5/2*a - ex+gohi+120id (?) o3o3o5/4x5/2*a - radatathi ``` otherWythoffians ```x3x3o5o5/3*a - gidpixathi x3o3x5o5/3*a - (contains cadditradid) x3o3o5x5/3*a - gixhidy o3x3x5o5/3*a - sidpixathi o3x3o5x5/3*a - sirfixthi o3o3x5x5/3*a - sixhidy x3x3x5o5/3*a - (contains cadditradid) x3x3o5x5/3*a - sixathi x3o3x5x5/3*a - hixady o3x3x5x5/3*a - gixathi x3x3x5x5/3*a - xithi ``` ```x3/2x3o5o5/2*a - [Grünbaumian] x3/2o3x5o5/2*a - (contains "2thah") x3/2o3o5x5/2*a - [Grünbaumian] o3/2x3x5o5/2*a - sidpixathi o3/2x3o5x5/2*a - sirfixthi o3/2o3x5x5/2*a - sixhidy x3/2x3x5o5/2*a - [Grünbaumian] x3/2x3o5x5/2*a - [Grünbaumian] x3/2o3x5x5/2*a - [Grünbaumian] o3/2x3x5x5/2*a - gixathi x3/2x3x5x5/2*a - [Grünbaumian] ``` ```x3x3/2o5o5/2*a - gidpixathi x3o3/2x5o5/2*a - (contains "2thah") x3o3/2o5x5/2*a - [Grünbaumian] o3x3/2x5o5/2*a - [Grünbaumian] o3x3/2o5x5/2*a - (contains sicdatrid) o3o3/2x5x5/2*a - sixhidy x3x3/2x5o5/2*a - [Grünbaumian] x3x3/2o5x5/2*a - [Grünbaumian] x3o3/2x5x5/2*a - [Grünbaumian] o3x3/2x5x5/2*a - [Grünbaumian] x3x3/2x5x5/2*a - [Grünbaumian] ``` ```x3x3o5/4o5/2*a - gidpixathi x3o3x5/4o5/2*a - (contains cadditradid) x3o3o5/4x5/2*a - [Grünbaumian] o3x3x5/4o5/2*a - sidpixathi o3x3o5/4x5/2*a - (contains sicdatrid) o3o3x5/4x5/2*a - [Grünbaumian] x3x3x5/4o5/2*a - (contains cadditradid) x3x3o5/4x5/2*a - [Grünbaumian] x3o3x5/4x5/2*a - [Grünbaumian] o3x3x5/4x5/2*a - [Grünbaumian] x3x3x5/4x5/2*a - [Grünbaumian] ``` (partial)snubs andholosnubs ```... ``` ```... ``` ```... ``` ```... ``` o3/2o3/2o5o5/3*a (µ=1025) o3o3/2o5/4o5/3*a (µ=1505) o3/2o3o5/4o5/3*a (µ=1735) o3/2o3/2o5/4o5/2*a (µ=1975) quasiregulars ```x3/2o3/2o5o5/3*a - gax+gashi+120gid (?) o3/2x3/2o5o5/3*a - dittady+dox (?) o3/2o3/2x5o5/3*a - ex+gohi+120id (?) o3/2o3/2o5x5/3*a - radatathi ``` ```x3o3/2o5/4o5/3*a - gax+gashi+120gid (?) o3x3/2o5/4o5/3*a - dittady+dox (?) o3o3/2x5/4o5/3*a - ex+gohi+120id (?) o3o3/2o5/4x5/3*a - radatathi ``` ```x3/2o3o5/4o5/3*a - gax+gashi+120gid (?) o3/2x3o5/4o5/3*a - dittady+dox (?) o3/2o3x5/4o5/3*a - ex+gohi+120id (?) o3/2o3o5/4x5/3*a - radatathi ``` ```x3/2o3/2o5/4o5/2*a - gax+gashi+120gid (?) o3/2x3/2o5/4o5/2*a - dittady+dox (?) o3/2o3/2x5/4o5/2*a - ex+gohi+120id (?) o3/2o3/2o5/4x5/2*a - radatathi ``` otherWythoffians ```x3/2x3/2o5o5/3*a - [Grünbaumian] x3/2o3/2x5o5/3*a - (contains cadditradid) x3/2o3/2o5x5/3*a - gixhidy o3/2x3/2x5o5/3*a - [Grünbaumian] o3/2x3/2o5x5/3*a - (contains sicdatrid) o3/2o3/2x5x5/3*a - sixhidy x3/2x3/2x5o5/3*a - [Grünbaumian] x3/2x3/2o5x5/3*a - [Grünbaumian] x3/2o3/2x5x5/3*a - hixady o3/2x3/2x5x5/3*a - [Grünbaumian] x3/2x3/2x5x5/3*a - [Grünbaumian] ``` ```x3x3/2o5/4o5/3*a - gidpixathi x3o3/2x5/4o5/3*a - (contains "2thah") x3o3/2o5/4x5/3*a - gixhidy o3x3/2x5/4o5/3*a - [Grünbaumian] o3x3/2o5/4x5/3*a - sirfixthi o3o3/2x5/4x5/3*a - [Grünbaumian] x3x3/2x5/4o5/3*a - [Grünbaumian] x3x3/2o5/4x5/3*a - sixathi x3o3/2x5/4x5/3*a - [Grünbaumian] o3x3/2x5/4x5/3*a - [Grünbaumian] x3x3/2x5/4x5/3*a - [Grünbaumian] ``` ```x3/2x3o5/4o5/3*a - [Grünbaumian] x3/2o3x5/4o5/3*a - (contains "2thah") x3/2o3o5/4x5/3*a - gixhidy o3/2x3x5/4o5/3*a - sidpixathi o3/2x3o5/4x5/3*a - (contains sicdatrid) o3/2o3x5/4x5/3*a - [Grünbaumian] x3/2x3x5/4o5/3*a - [Grünbaumian] x3/2x3o5/4x5/3*a - [Grünbaumian] x3/2o3x5/4x5/3*a - [Grünbaumian] o3/2x3x5/4x5/3*a - [Grünbaumian] x3/2x3x5/4x5/3*a - [Grünbaumian] ``` ```x3/2x3/2o5/4o5/2*a - [Grünbaumian] x3/2o3/2x5/4o5/2*a - (contains cadditradid) x3/2o3/2o5/4x5/2*a - [Grünbaumian] o3/2x3/2x5/4o5/2*a - [Grünbaumian] o3/2x3/2o5/4x5/2*a - sirfixthi o3/2o3/2x5/4x5/2*a - [Grünbaumian] x3/2x3/2x5/4o5/2*a - [Grünbaumian] x3/2x3/2o5/4x5/2*a - [Grünbaumian] x3/2o3/2x5/4x5/2*a - [Grünbaumian] o3/2x3/2x5/4x5/2*a - [Grünbaumian] x3/2x3/2x5/4x5/2*a - [Grünbaumian] ``` (partial)snubs andholosnubs ```... ``` ```... ``` ```... ``` ```... ```

### Hecatonicosachoral ("hyic") Symmetries – type o5o5/2o5o5/3*a   (up)

 o5o5/2o5o5/3*a (µ=108) o5o5/2o5/4o5/2*a (µ=252) o5o5/3o5/4o5/3*a (µ=972) o5/4o5/2o5/4o5/3*a (µ=2268) quasiregulars ```x5o5/2o5o5/3*a - sishi+gaghi+120did (?) o5x5/2o5o5/3*a - sishi+gaghi+120did (?) ``` ```x5o5/2o5/4o5/2*a - sishi+gaghi+120did (?) o5o5/2x5/4o5/2*a - sishi+gaghi+120did (?) ``` ```x5o5/3o5/4o5/3*a - sishi+gaghi+120did (?) o5o5/3x5/4o5/3*a - sishi+gaghi+120did (?) ``` ```x5/4o5/2o5/4o5/3*a - sishi+gaghi+120did (?) o5/4x5/2o5/4o5/3*a - sishi+gaghi+120did (?) ``` otherWythoffians ```x5x5/2o5o5/3*a - 2giprapivady (?) x5o5/2x5o5/3*a - (contains cadditradid) x5o5/2o5x5/3*a - 2spapivady (?) o5x5/2x5o5/3*a - [Grünbaumian] x5x5/2x5o5/3*a - [Grünbaumian] x5x5/2o5x5/3*a - ebuthi x5x5/2x5x5/3*a - [Grünbaumian] ``` ```x5x5/2o5/4o5/2*a - 2giprapivady (?) x5o5/2x5/4o5/2*a - (contains cadditradid) x5o5/2o5/4x5/2*a - [Grünbaumian] o5o5/2x5/4x5/2*a - [Grünbaumian] x5x5/2x5/4o5/2*a - [Grünbaumian] x5o5/2x5/4x5/2*a - [Grünbaumian] x5x5/2x5/4x5/2*a - [Grünbaumian] ``` ```x5x5/3o5/4o5/3*a - 2giprapivady (?) x5o5/3x5/4o5/3*a - (contains cadditradid) x5o5/3o5/4x5/3*a - 2spapivady (?) o5o5/3x5/4x5/3*a - [Grünbaumian] x5x5/3x5/4o5/3*a - ebuthi x5o5/3x5/4x5/3*a - [Grünbaumian] x5x5/3x5/4x5/3*a - [Grünbaumian] ``` ```x5/4x5/2o5/4o5/3*a - [Grünbaumian] x5/4o5/2x5/4o5/3*a - (contains cadditradid) x5/4o5/2o5/4x5/3*a - 2spapivady (?) o5/4x5/2x5/4o5/3*a - [Grünbaumian] x5/4x5/2x5/4o5/3*a - [Grünbaumian] x5/4x5/2o5/4x5/3*a - [Grünbaumian] x5/4x5/2x5/4x5/3*a - [Grünbaumian] ``` (partial)snubs andholosnubs ```... ``` ```... ``` ```... ``` ```... ```