```
----
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

 linear ones ```o-P-o-Q-o-R-o ```

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

 o3o3o3o (convex) o3o3o3/2o (µ=4) o3o3/2o3o (µ=6) quasiregulars ```x3o3o3o - pen o3x3o3o - rap ``` ```x3o3o3/2o - pen o3x3o3/2o - rap o3o3x3/2o - rap o3o3o3/2x - pen ``` ```x3o3/2o3o - pen o3x3/2o3o - rap ``` otherWythoffians ```x3x3o3o - tip x3o3x3o - srip x3o3o3x - spid o3x3x3o - deca x3x3x3o - grip x3x3o3x - prip x3x3x3x - gippid ``` ```x3x3o3/2o - tip x3o3x3/2o - srip x3o3o3/2x - 2firp (?) o3x3x3/2o - deca o3x3o3/2x - pinnip+5 2thah (?) o3o3x3/2x - [Grünbaumian] x3x3x3/2o - grip x3x3o3/2x - pirpop+5 2thah (?) x3o3x3/2x - [Grünbaumian] o3x3x3/2x - [Grünbaumian] x3x3x3/2x - [Grünbaumian] ``` ```x3x3/2o3o - tip x3o3/2x3o - pinnip+5 2thah (?) x3o3/2o3x - 2firp (?) o3x3/2x3o - [Grünbaumian] x3x3/2x3o - [Grünbaumian] x3x3/2o3x - pirpop+5 2thah (?) x3x3/2x3x - [Grünbaumian] ``` (partial)snubs andholosnubs ```β3o3o3o - 3pen (?) o3β3o3o - firp+rap+15{4} (?) β3x3o3o - 2rap (?) x3β3o3o - (?) *) β3β3o3o - 2rap+20tet (?) β3o3x3o - rawvtip x3o3β3o - pinnipdip+15{4} (?) β3o3β3o - (?) *) β3o3o3x - piphid+10tet (?) β3o3o3β - 4pen+160{3} (?) o3β3x3o - (?) *) o3β3β3o - (?) *) β3x3x3o - 2deca (?) x3β3x3o - 2srip (?) x3x3β3o - (?) *) β3β3x3o - 2srip (?) β3x3β3o - (?) *) x3β3β3o - 2srip+20trip (?) β3β3β3o - (?) *) β3x3o3x - 2srip (?) x3β3o3x - (?) *) x3x3o3β - pittip β3β3o3x - 2srip+20{6}+40{3} (?) **) β3x3o3β - 2srip+20{6}+60{3} (?) **) x3β3o3β - (?) *) β3β3o3β - (?) *) β3x3x3x - 2grip (?) x3β3x3x - 2prip (?) β3β3x3x - 2prip (?) β3x3β3x - (?) *) β3x3x3β - (?) *) x3β3β3x - (?) *) β3β3β3x - (?) *) β3β3x3β - (?) *) s3s3s3s - snip *) ``` ```... ``` ```... ``` o3o3/2o3/2o (µ=9) o3/2o3o3/2o (µ=11) o3/2o3/2o3/2o (µ=16) quasiregulars ```x3o3/2o3/2o - pen o3x3/2o3/2o - rap o3o3/2x3/2o - rap o3o3/2o3/2x - pen ``` ```x3/2o3o3/2o - pen o3/2x3o3/2o - rap ``` ```x3/2o3/2o3/2o - pen o3/2x3/2o3/2o - rap ``` otherWythoffians ```x3x3/2o3/2o - tip x3o3/2x3/2o - pinnip+5 2thah (?) x3o3/2o3/2x - spid o3x3/2x3/2o - [Grünbaumian] o3x3/2o3/2x - srip o3o3/2x3/2x - [Grünbaumian] x3x3/2x3/2o - [Grünbaumian] x3x3/2o3/2x - prip x3o3/2x3/2x - [Grünbaumian] o3x3/2x3/2x - [Grünbaumian] x3x3/2x3/2x - [Grünbaumian] ``` ```x3/2x3o3/2o - [Grünbaumian] x3/2o3x3/2o - pinnip+5 2thah (?) x3/2o3o3/2x - spid o3/2x3x3/2o - deca x3/2x3x3/2o - [Grünbaumian] x3/2x3o3/2x - [Grünbaumian] x3/2x3x3/2x - [Grünbaumian] ``` ```x3/2x3/2o3/2o - [Grünbaumian] x3/2o3/2x3/2o - srip x3/2o3/2o3/2x - 2firp (?) o3/2x3/2x3/2o - [Grünbaumian] x3/2x3/2x3/2o - [Grünbaumian] x3/2x3/2o3/2x - [Grünbaumian] x3/2x3/2x3/2x - [Grünbaumian] ``` (partial)snubs andholosnubs ```... ``` ```... ``` ```... ```

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

 o3o3o4o (convex) o3/2o3o4o (µ=7) o3o3o4/3o (µ=15) o3o3/2o4o (µ=17) quasiregulars ```x3o3o4o - hex o3x3o4o - ico o3o3x4o - rit o3o3o4x - tes ``` ```x3/2o3o4o - hex o3/2x3o4o - ico o3/2o3x4o - rit o3/2o3o4x - tes ``` ```x3o3o4/3o - hex o3x3o4/3o - ico o3o3x4/3o - rit o3o3o4/3x - tes ``` ```x3o3/2o4o - hex o3x3/2o4o - ico o3o3/2x4o - rit o3o3/2o4x - tes ``` otherWythoffians ```x3x3o4o - thex x3o3x4o - rico x3o3o4x - sidpith o3x3x4o - tah o3x3o4x - srit o3o3x4x - tat x3x3x4o - tico x3x3o4x - prit x3o3x4x - proh o3x3x4x - grit x3x3x4x - gidpith ``` ```x3/2x3o4o - [Grünbaumian] x3/2o3x4o - 2huhoh+3tes+8co (?) x3/2o3o4x - quidpith o3/2x3x4o - tah o3/2x3o4x - srit o3/2o3x4x - tat x3/2x3x4o - [Grünbaumian] x3/2x3o4x - [Grünbaumian] x3/2o3x4x - spript+16 2thah (?) o3/2x3x4x - grit x3/2x3x4x - [Grünbaumian] ``` ```x3x3o4/3o - thex x3o3x4/3o - rico x3o3o4/3x - quidpith o3x3x4/3o - tah o3x3o4/3x - qrit o3o3x4/3x - quitit x3x3x4/3o - tico x3x3o4/3x - paqrit x3o3x4/3x - quiproh o3x3x4/3x - gaqrit x3x3x4/3x - gaquidpoth ``` ```x3x3/2o4o - thex x3o3/2x4o - 2huhoh+3tes+8co (?) x3o3/2o4x - quidpith o3x3/2x4o - [Grünbaumian] o3x3/2o4x - qrit o3o3/2x4x - tat x3x3/2x4o - [Grünbaumian] x3x3/2o4x - paqrit x3o3/2x4x - spript+16 2thah (?) o3x3/2x4x - [Grünbaumian] x3x3/2x4x - [Grünbaumian] ``` (partial)snubs andholosnubs ```β3o3o4o - 2hex+8oct (?) o3β3o4o - ico+gico+72{4} (?) o3o3β4o - (?) *) o3o3o4s - hex o3o3o4β - haddet β3x3o4o - 2ico (?) x3β3o4o - (?) *) β3β3o4o - 2ico+48{4}+128{3} (?) **) β3o3x4o - rawvhitto x3o3β4o - (?) *) β3o3β4o - (?) *) β3o3o4x - shafipto+32tet (?) β3o3o4β - (?) *) x3o3o4s - rit o3β3x4o - (?) *) o3x3β4o - (?) *) o3β3β4o - (?) *) o3β3o4x - pinpith+48{4} (?) o3x3o4s - thex o3β3o4β - (?) *) o3o3β4x - (?) *) o3o3x4s - rit o3o3β4β - 2rit+64tet (?) β3x3x4o - 2tah (?) x3β3x4o - 2rico (?) x3x3β4o - (?) *) β3β3x4o - 2rico (?) β3x3β4o - (?) *) x3β3β4o - (?) *) s3s3s4o - sadi β3x3o4x - 2srit (?) x3β3o4x - (?) *) x3x3o4s - tah β3β3o4x - 2srit+48{8}+128{3} (?) **) β3x3o4β - (?) *) x3β3o4β - (?) *) β3β3o4β - (?) *) β3o3x4x - siphado x3o3β4x - (?) *) x3o3x4s - rico β3o3β4x - (?) *) β3o3x4β - 2rico+64{6}+192{3} (?) **) x3o3β4β - 2rico+64{6}+128{3} (?) **) β3o3β4β - (?) *) o3β3x4x - (?) *) o3x3β4x - 2srit (?) o3x3x4s - tah o3β3β4x - 2srit+64trip (?) o3β3x4β - (?) *) o3x3β4β - 2srit (?) o3β3β4β - (?) *) β3x3x4x - 2grit (?) x3β3x4x - 2proh (?) x3x3β4x - 2prit (?) x3x3x4s - tico β3β3x4x - 2proh (?) β3x3β4x - (?) *) β3x3x4β - (?) *) x3β3β4x - (?) *) x3β3x4β - (?) *) x3x3β4β - 2prit (?) s3s3s4x - (?) *) β3β3x4β - (?) *) β3x3β4β - (?) *) x3β3β4β - (?) *) s3s3s4s - snet *) ``` ```... ``` ```... ``` ```... ``` o3/2o3/2o4o (µ=23) o3o3/2o4/3o (µ=31) o3/2o3o4/3o (µ=41) o3/2o3/2o4/3o (µ=57) quasiregulars ```x3/2o3/2o4o - hex o3/2x3/2o4o - ico o3/2o3/2x4o - rit o3/2o3/2o4x - tes ``` ```x3o3/2o4/3o - hex o3x3/2o4/3o - ico o3o3/2x4/3o - rit o3o3/2o4/3x - tes ``` ```x3/2o3o4/3o - hex o3/2x3o4/3o - ico o3/2o3x4/3o - rit o3/2o3o4/3x - tes ``` ```x3/2o3/2o4/3o - hex o3/2x3/2o4/3o - ico o3/2o3/2x4/3o - rit o3/2o3/2o4/3x - tes ``` otherWythoffians ```x3/2x3/2o4o - [Grünbaumian] x3/2o3/2x4o - rico x3/2o3/2o4x - sidpith o3/2x3/2x4o - [Grünbaumian] o3/2x3/2o4x - qrit o3/2o3/2x4x - tat x3/2x3/2x4o - [Grünbaumian] x3/2x3/2o4x - [Grünbaumian] x3/2o3/2x4x - proh o3/2x3/2x4x - [Grünbaumian] x3/2x3/2x4x - [Grünbaumian] ``` ```x3x3/2o4/3o - thex x3o3/2x4/3o - 2huhoh+3tes+8co (?) x3o3/2o4/3x - sidpith o3x3/2x4/3o - [Grünbaumian] o3x3/2o4/3x - srit o3o3/2x4/3x - quitit x3x3/2x4/3o - [Grünbaumian] x3x3/2o4/3x - prit x3o3/2x4/3x - gapript+16 2thah (?) o3x3/2x4/3x - [Grünbaumian] x3x3/2x4/3x - [Grünbaumian] ``` ```x3/2x3o4/3o - [Grünbaumian] x3/2o3x4/3o - 2huhoh+3tes+8co (?) x3/2o3o4/3x - sidpith o3/2x3x4/3o - tah o3/2x3o4/3x - qrit o3/2o3x4/3x - quitit x3/2x3x4/3o - [Grünbaumian] x3/2x3o4/3x - [Grünbaumian] x3/2o3x4/3x - gapript+16 2thah (?) o3/2x3x4/3x - gaqrit x3/2x3x4/3x - [Grünbaumian] ``` ```x3/2x3/2o4/3o - [Grünbaumian] x3/2o3/2x4/3o - rico x3/2o3/2o4/3x - quidpith o3/2x3/2x4/3o - [Grünbaumian] o3/2x3/2o4/3x - srit o3/2o3/2x4/3x - quitit x3/2x3/2x4/3o - [Grünbaumian] x3/2x3/2o4/3x - [Grünbaumian] x3/2o3/2x4/3x - quiproh o3/2x3/2x4/3x - [Grünbaumian] x3/2x3/2x4/3x - [Grünbaumian] ``` (partial)snubs andholosnubs ```s3/2s3/2s4o - rasdi ... ``` ```... ``` ```... ``` ```... ```

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

 o3o4o3o (convex) o3o4o3/2o (µ=23) o3o4/3o3o (µ=73) quasiregulars ```x3o4o3o - ico o3x4o3o - rico ``` ```x3o4o3/2o - ico o3x4o3/2o - rico o3o4x3/2o - rico o3o4o3/2x - ico ``` ```x3o4/3o3o - ico o3x4/3o3o - rico ``` otherWythoffians ```x3x4o3o - tico x3o4x3o - srico x3o4o3x - spic o3x4x3o - cont x3x4x3o - grico x3x4o3x - prico x3x4x3x - gippic ``` ```x3x4o3/2o - tico x3o4x3/2o - srico x3o4o3/2x - quippic o3x4x3/2o - cont o3x4o3/2x - qrico o3o4x3/2x - [Grünbaumian] x3x4x3/2o - grico x3x4o3/2x - paqri x3o4x3/2x - [Grünbaumian] o3x4x3/2x - [Grünbaumian] x3x4x3/2x - [Grünbaumian] ``` ```x3x4/3o3o - tico x3o4/3x3o - qrico x3o4/3o3x - quippic o3x4/3x3o - gic x3x4/3x3o - gaqri x3x4/3o3x - paqri x3x4/3x3x - gaquapac ``` (partial)snubs andholosnubs ```β3o4o3o - ico+gico+72{4} (?) o3β4o3o - (?) *) β3x4o3o - 2rico (?) x3β4o3o - (?) *) s3s4o3o - sadi β3o4x3o - rawvaty x3o4β3o - (?) *) β3o4β3o - (?) *) β3o4o3x - inpac+72{4} (?) β3o4o3β - (?) *) o3β4x3o - (?) *) o3β4β3o - (?) *) β3x4x3o - 2cont (?) x3β4x3o - 2srico (?) x3x4β3o - (?) *) s3s4x3o - srico β3x4β3o - (?) *) x3β4β3o - 2srico+192trip (?) β3β4β3o - (?) *) β3x4o3x - 2srico (?) x3β4o3x - (?) *) x3x4o3β - sipti s3s4o3x - prissi **) β3x4o3β - 2srico+144{8}+576{3} (?) **) x3β4o3β - (?) *) β3β4o3β - (?) *) β3x4x3x - 2grico (?) x3β4x3x - 2prico (?) s3s4x3x - prico β3x4β3x - (?) *) β3x4x3β - (?) *) x3β4β3x - (?) *) β3β4β3x - (?) *) β3β4x3β - (?) *) s3s4s3s - snico *) ``` ```o3o4s3/2s - rasdi x3o4s3/2s - prarsi **) ... ``` ```... ``` o3o4/3o3/2o (µ=95) o3/2o4o3/2o (µ=97) o3/2o4/3o3/2o (µ=169) quasiregulars ```x3o4/3o3/2o - ico o3x4/3o3/2o - rico o3o4/3x3/2o - rico o3o4/3o3/2x - ico ``` ```x3/2o4o3/2o - ico o3/2x4o3/2o - rico ``` ```x3/2o4/3o3/2o - ico o3/2x4/3o3/2o - rico ``` otherWythoffians ```x3x4/3o3/2o - tico x3o4/3x3/2o - qrico x3o4/3o3/2x - spic o3x4/3x3/2o - gic o3x4/3o3/2x - srico o3o4/3x3/2x - [Grünbaumian] x3x4/3x3/2o - gaqri x3x4/3o3/2x - prico x3o4/3x3/2x - [Grünbaumian] o3x4/3x3/2x - [Grünbaumian] x3x4/3x3/2x - [Grünbaumian] ``` ```x3/2x4o3/2o - [Grünbaumian] x3/2o4x3/2o - qrico x3/2o4o3/2x - spic o3/2x4x3/2o - cont x3/2x4x3/2o - [Grünbaumian] x3/2x4o3/2x - [Grünbaumian] x3/2x4x3/2x - [Grünbaumian] ``` ```x3/2x4/3o3/2o - [Grünbaumian] x3/2o4/3x3/2o - srico x3/2o4/3o3/2x - quippic o3/2x4/3x3/2o - gic x3/2x4/3x3/2o - [Grünbaumian] x3/2x4/3o3/2x - [Grünbaumian] x3/2x4/3x3/2x - [Grünbaumian] ``` (partial)snubs andholosnubs ```... ``` ```... ``` ```... ```

### Hecatonicosachoral ("hyic") Symmetries – type o3o3o5o   (up)

 o3o3o5o (convex) o3/2o3o5o (µ=119) o3o3o5/4o (µ=599) o3o3/2o5o (µ=601) quasiregulars ```x3o3o5o - ex o3x3o5o - rox o3o3x5o - rahi o3o3o5x - hi ``` ```x3/2o3o5o - ex o3/2x3o5o - rox o3/2o3x5o - rahi o3/2o3o5x - hi ``` ```x3o3o5/4o - ex o3x3o5/4o - rox o3o3x5/4o - rahi o3o3o5/4x - hi ``` ```x3o3/2o5o - ex o3x3/2o5o - rox o3o3/2x5o - rahi o3o3/2o5x - hi ``` otherWythoffians ```x3x3o5o - tex x3o3x5o - srix x3o3o5x - sidpixhi o3x3x5o - xhi o3x3o5x - srahi o3o3x5x - thi x3x3x5o - grix x3x3o5x - prahi x3o3x5x - prix o3x3x5x - grahi x3x3x5x - gidpixhi ``` ```x3/2x3o5o - 3ex+fix (?) x3/2o3x5o - frox+600 2thah (?) x3/2o3o5x - saquid paxhi o3/2x3x5o - xhi o3/2x3o5x - srahi o3/2o3x5x - thi x3/2x3x5o - [Grünbaumian] x3/2x3o5x - [Grünbaumian] x3/2o3x5x - spriphi+600 2thah (?) o3/2x3x5x - grahi x3/2x3x5x - [Grünbaumian] ``` ```x3x3o5/4o - tex x3o3x5/4o - srix x3o3o5/4x - saquid paxhi o3x3x5/4o - xhi o3x3o5/4x - (contains gicdatrid) o3o3x5/4x - [Grünbaumian] x3x3x5/4o - grix x3x3o5/4x - (contains gicdatrid) x3o3x5/4x - [Grünbaumian] o3x3x5/4x - [Grünbaumian] x3x3x5/4x - [Grünbaumian] ``` ```x3x3/2o5o - tex x3o3/2x5o - frox+600 2thah (?) x3o3/2o5x - saquid paxhi o3x3/2x5o - 3ex+2fix+gaghi (?) o3x3/2o5x - (contains gicdatrid) o3o3/2x5x - thi x3x3/2x5o - [Grünbaumian] x3x3/2o5x - (contains gicdatrid) x3o3/2x5x - spriphi+600 2thah (?) o3x3/2x5x - [Grünbaumian] x3x3/2x5x - [Grünbaumian] ``` (partial)snubs andholosnubs ```β3o3o5o - 2ex+120ike (?) o3β3o5o - rox+720pip (?) o3o3β5o - (?) *) o3o3o5β - sidtaxhi β3x3o5o - 2rox (?) x3β3o5o - (?) *) β3β3o5o - 2rox+1440{5}+2400{3} (?) **) β3o3x5o - srawv hixhi x3o3β5o - (?) *) β3o3β5o - (?) *) β3o3o5x - six fipady+1200tet (?) x3o3o5β - stut phiddix β3o3o5β - (?) *) o3β3x5o - (?) *) o3x3β5o - (?) *) o3β3β5o - (?) *) o3β3o5x - pinpixhi+1800{4} (?) o3x3o5β - wavhiddix o3β3o5β - (?) *) o3o3β5x - (?) *) o3o3x5β - 2rahi (?) o3o3β5β - 2rahi+2400tet (?) β3x3x5o - 2xhi (?) x3β3x5o - 2srix (?) x3x3β5o - (?) *) β3β3x5o - 2srix (?) β3x3β5o - (?) *) x3β3β5o - (?) *) β3β3β5o - (?) *) β3x3o5x - 2srahi (?) x3β3o5x - (?) *) x3x3o5β - sphiddix β3β3o5x - 2srahi+1440{10}+4800{3} (?) **) β3x3o5β - (?) *) x3β3o5β - (?) *) β3β3o5β - (?) *) β3o3x5x - spixhihy x3o3β5x - (?) *) x3o3x5β - 2srix (?) β3o3β5x - (?) *) β3o3x5β - 2srix+2400{6}+7200{3} (?) **) x3o3β5β - 2srix+2400{6}+4800{3} (?) **) β3o3β5β - (?) *) o3β3x5x - (?) *) o3x3β5x - 2srahi (?) o3x3x5β - 2xhi (?) o3β3β5x - 2srahi+2400trip (?) o3β3x5β - (?) *) o3x3β5β - 2srahi (?) o3β3β5β - (?) *) β3x3x5x - 2grahi (?) x3β3x5x - 2prix (?) x3x3β5x - 2prahi (?) x3x3x5β - 2grix (?) β3β3x5x - 2prix (?) β3x3β5x - (?) *) β3x3x5β - (?) *) x3β3β5x - (?) *) x3β3x5β - (?) *) x3x3β5β - 2prahi (?) β3β3β5x - (?) *) β3β3x5β - (?) *) β3x3β5β - (?) *) x3β3β5β - (?) *) s3s3s5s - snahi *) ``` ```... ``` ```... ``` ```... ``` o3/2o3/2o5o (µ=719) o3o3/2o5/4o (µ=1199) o3/2o3o5/4o (µ=1681) o3/2o3/2o5/4o (µ=2281) quasiregulars ```x3/2o3/2o5o - ex o3/2x3/2o5o - rox o3/2o3/2x5o - rahi o3/2o3/2o5x - hi ``` ```x3o3/2o5/4o - ex o3x3/2o5/4o - rox o3o3/2x5/4o - rahi o3o3/2o5/4x - hi ``` ```x3/2o3o5/4o - ex o3/2x3o5/4o - rox o3/2o3x5/4o - rahi o3/2o3o5/4x - hi ``` ```x3/2o3/2o5/4o - ex o3/2x3/2o5/4o - rox o3/2o3/2x5/4o - rahi o3/2o3/2o5/4x - hi ``` otherWythoffians ```x3/2x3/2o5o - 3ex+fix (?) x3/2o3/2x5o - srix x3/2o3/2o5x - sidpixhi o3/2x3/2x5o - 3ex+2fix+gaghi (?) o3/2x3/2o5x - (contains gicdatrid) o3/2o3/2x5x - thi x3/2x3/2x5o - 2rox+sophi (?) x3/2x3/2o5x - [Grünbaumian] x3/2o3/2x5x - prix o3/2x3/2x5x - [Grünbaumian] x3/2x3/2x5x - [Grünbaumian] ``` ```x3x3/2o5/4o - tex x3o3/2x5/4o - frox+600 2thah (?) x3o3/2o5/4x - sidpixhi o3x3/2x5/4o - 3ex+2fix+gaghi (?) o3x3/2o5/4x - srahi o3o3/2x5/4x - [Grünbaumian] x3x3/2x5/4o - [Grünbaumian] x3x3/2o5/4x - prahi x3o3/2x5/4x - [Grünbaumian] o3x3/2x5/4x - [Grünbaumian] x3x3/2x5/4x - [Grünbaumian] ``` ```x3/2x3o5/4o - 3ex+fix (?) x3/2o3x5/4o - frox+600 2thah (?) x3/2o3o5/4x - sidpixhi o3/2x3x5/4o - xhi o3/2x3o5/4x - (contains gicdatrid) o3/2o3x5/4x - [Grünbaumian] x3/2x3x5/4o - [Grünbaumian] x3/2x3o5/4x - [Grünbaumian] x3/2o3x5/4x - [Grünbaumian] o3/2x3x5/4x - [Grünbaumian] x3/2x3x5/4x - [Grünbaumian] ``` ```x3/2x3/2o5/4o - 3ex+fix (?) x3/2o3/2x5/4o - srix x3/2o3/2o5/4x - saquid paxhi o3/2x3/2x5/4o - 3ex+2fix+gaghi (?) o3/2x3/2o5/4x - srahi o3/2o3/2x5/4x - [Grünbaumian] x3/2x3/2x5/4o - 2rox+sophi (?) x3/2x3/2o5/4x - [Grünbaumian] x3/2o3/2x5/4x - [Grünbaumian] o3/2x3/2x5/4x - [Grünbaumian] x3/2x3/2x5/4x - [Grünbaumian] ``` (partial)snubs andholosnubs ```... ``` ```... ``` ```... ``` ```... ```

### Hecatonicosachoral ("hyic") Symmetries – type o3o3o5/2o   (up)

 o3o3o5/2o (µ=191) o3o3o5/3o (µ=409) o3/2o3o5/2o (µ=649) o3o3/2o5/2o (µ=791) quasiregulars ```x3o3o5/2o - gax o3x3o5/2o - raggix o3o3x5/2o - rigogishi o3o3o5/2x - gogishi ``` ```x3o3o5/3o - gax o3x3o5/3o - raggix o3o3x5/3o - rigogishi o3o3o5/3x - gogishi ``` ```x3/2o3o5/2o - gax o3/2x3o5/2o - raggix o3/2o3x5/2o - rigogishi o3/2o3o5/2x - gogishi ``` ```x3o3/2o5/2o - gax o3x3/2o5/2o - raggix o3o3/2x5/2o - rigogishi o3o3/2o5/2x - gogishi ``` otherWythoffians ```x3x3o5/2o - taggix x3o3x5/2o - sirgax x3o3o5/2x - quad pagaxhi o3x3x5/2o - gixhi o3x3o5/2x - (contains sicdatrid) o3o3x5/2x - [Grünbaumian] x3x3x5/2o - graggix x3x3o5/2x - (contains sicdatrid) x3o3x5/2x - [Grünbaumian] o3x3x5/2x - [Grünbaumian] x3x3x5/2x - [Grünbaumian] ``` ```x3x3o5/3o - taggix x3o3x5/3o - sirgax x3o3o5/3x - quidpixhi o3x3x5/3o - gixhi o3x3o5/3x - qrahi o3o3x5/3x - quit gogishi x3x3x5/3o - graggix x3x3o5/3x - paqrigagishi x3o3x5/3x - quippirgax o3x3x5/3x - gaqrigagishi x3x3x5/3x - gaquidapixhi ``` ```x3/2x3o5/2o - [Grünbaumian] x3/2o3x5/2o - ripahi+600 2thah (?) x3/2o3o5/2x - quidpixhi o3/2x3x5/2o - gixhi o3/2x3o5/2x - (contains sicdatrid) o3/2o3x5/2x - [Grünbaumian] x3/2x3x5/2o - [Grünbaumian] x3/2x3o5/2x - [Grünbaumian] x3/2o3x5/2x - [Grünbaumian] o3/2x3x5/2x - [Grünbaumian] x3/2x3x5/2x - [Grünbaumian] ``` ```x3x3/2o5/2o - taggix x3o3/2x5/2o - ripahi+600 2thah (?) x3o3/2o5/2x - quidpixhi o3x3/2x5/2o - [Grünbaumian] o3x3/2o5/2x - qrahi o3o3/2x5/2x - [Grünbaumian] x3x3/2x5/2o - [Grünbaumian] x3x3/2o5/2x - paqrigagishi x3o3/2x5/2x - [Grünbaumian] o3x3/2x5/2x - [Grünbaumian] x3x3/2x5/2x - [Grünbaumian] ``` (partial)snubs andholosnubs ```... ``` ```... ``` ```... ``` ```... ``` o3o3/2o5/3o (µ=1009) o3/2o3o5/3o (µ=1151) o3/2o3/2o5/2o (µ=1249) o3/2o3/2o5/3o (µ=1751) quasiregulars ```x3o3/2o5/3o - gax o3x3/2o5/3o - raggix o3o3/2x5/3o - rigogishi o3o3/2o5/3x - gogishi ``` ```x3/2o3o5/3o - gax o3/2x3o5/3o - raggix o3/2o3x5/3o - rigogishi o3/2o3o5/3x - gogishi ``` ```x3/2o3/2o5/2o - gax o3/2x3/2o5/2o - raggix o3/2o3/2x5/2o - rigogishi o3/2o3/2o5/2x - gogishi ``` ```x3/2o3/2o5/3o - gax o3/2x3/2o5/3o - raggix o3/2o3/2x5/3o - rigogishi o3/2o3/2o5/3x - gogishi ``` otherWythoffians ```x3x3/2o5/3o - taggix x3o3/2x5/3o - ripahi+600 2thah (?) x3o3/2o5/3x - quad pagaxhi o3x3/2x5/3o - [Grünbaumian] o3x3/2o5/3x - (contains sicdatrid) o3o3/2x5/3x - quit gogishi x3x3/2x5/3o - [Grünbaumian] x3x3/2o5/3x - (contains sicdatrid) x3o3/2x5/3x - gipriphi+600 2thah (?) o3x3/2x5/3x - [Grünbaumian] x3x3/2x5/3x - [Grünbaumian] ``` ```x3/2x3o5/3o - [Grünbaumian] x3/2o3x5/3o - ripahi+600 2thah (?) x3/2o3o5/3x - quad pagaxhi o3/2x3x5/3o - gixhi o3/2x3o5/3x - qrahi o3/2o3x5/3x - quit gogishi x3/2x3x5/3o - [Grünbaumian] x3/2x3o5/3x - [Grünbaumian] x3/2o3x5/3x - gipriphi+600 2thah (?) o3/2x3x5/3x - gaqrigagishi x3/2x3x5/3x - [Grünbaumian] ``` ```x3/2x3/2o5/2o - [Grünbaumian] x3/2o3/2x5/2o - sirgax x3/2o3/2o5/2x - quad pagaxhi o3/2x3/2x5/2o - [Grünbaumian] o3/2x3/2o5/2x - qrahi o3/2o3/2x5/2x - [Grünbaumian] x3/2x3/2x5/2o - [Grünbaumian] x3/2x3/2o5/2x - [Grünbaumian] x3/2o3/2x5/2x - [Grünbaumian] o3/2x3/2x5/2x - [Grünbaumian] x3/2x3/2x5/2x - [Grünbaumian] ``` ```x3/2x3/2o5/3o - [Grünbaumian] x3/2o3/2x5/3o - sirgax x3/2o3/2o5/3x - quidpixhi o3/2x3/2x5/3o - [Grünbaumian] o3/2x3/2o5/3x - (contains sicdatrid) o3/2o3/2x5/3x - quit gogishi x3/2x3/2x5/3o - [Grünbaumian] x3/2x3/2o5/3x - [Grünbaumian] x3/2o3/2x5/3x - quippirgax o3/2x3/2x5/3x - [Grünbaumian] x3/2x3/2x5/3x - [Grünbaumian] ``` (partial)snubs andholosnubs ```... ``` ```... ``` ```... ``` ```... ```

### Hecatonicosachoral ("hyic") Symmetries – type o3o5o5/2o   (up)

 o3o5o5/2o (µ=4) o3o5o5/3o (µ=116) o3/2o5o5/2o (µ=356) o3/2o5o5/3o (µ=964) quasiregulars ```x3o5o5/2o - fix o3x5o5/2o - rofix o3o5x5/2o - rasishi o3o5o5/2x - sishi ``` ```x3o5o5/3o - fix o3x5o5/3o - rofix o3o5x5/3o - rasishi o3o5o5/3x - sishi ``` ```x3/2o5o5/2o - fix o3/2x5o5/2o - rofix o3/2o5x5/2o - rasishi o3/2o5o5/2x - sishi ``` ```x3/2o5o5/3o - fix o3/2x5o5/3o - rofix o3/2o5x5/3o - rasishi o3/2o5o5/3x - sishi ``` otherWythoffians ```x3x5o5/2o - tiffix x3o5x5/2o - sirfix x3o5o5/2x - padohi o3x5x5/2o - shihi o3x5o5/2x - sirsashi o3o5x5/2x - [Grünbaumian] x3x5x5/2o - girfix x3x5o5/2x - pirshi x3o5x5/2x - [Grünbaumian] o3x5x5/2x - [Grünbaumian] x3x5x5/2x - [Grünbaumian] ``` ```x3x5o5/3o - tiffix x3o5x5/3o - sirfix x3o5o5/3x - sishi+paphicki+gridaphi (?) o3x5x5/3o - shihi o3x5o5/3x - (contains cadditradid) o3o5x5/3x - quit sishi x3x5x5/3o - girfix x3x5o5/3x - (contains cadditradid) x3o5x5/3x - quippirfix o3x5x5/3x - gaqrisashi x3x5x5/3x - goquidipdy ``` ```x3/2x5o5/2o - [Grünbaumian] x3/2o5x5/2o - (contains gicdatrid) x3/2o5o5/2x - sishi+paphicki+gridaphi (?) o3/2x5x5/2o - shihi o3/2x5o5/2x - sirsashi o3/2o5x5/2x - [Grünbaumian] x3/2x5x5/2o - [Grünbaumian] x3/2x5o5/2x - [Grünbaumian] x3/2o5x5/2x - [Grünbaumian] o3/2x5x5/2x - [Grünbaumian] x3/2x5x5/2x - [Grünbaumian] ``` ```x3/2x5o5/3o - [Grünbaumian] x3/2o5x5/3o - (contains gicdatrid) x3/2o5o5/3x - padohi o3/2x5x5/3o - shihi o3/2x5o5/3x - (contains cadditradid) o3/2o5x5/3x - quit sishi x3/2x5x5/3o - [Grünbaumian] x3/2x5o5/3x - [Grünbaumian] x3/2o5x5/3x - (contains gicdatrid) o3/2x5x5/3x - gaqrisashi x3/2x5x5/3x - [Grünbaumian] ``` (partial)snubs andholosnubs ```... ``` ```... ``` ```... ``` ```... ``` o3o5/4o5/2o (µ=1084) o3o5/4o5/3o (µ=1196) o3/2o5/4o5/2o (µ=1436) o3/2o5/4o5/3o (µ=2044) quasiregulars ```x3o5/4o5/2o - fix o3x5/4o5/2o - rofix o3o5/4x5/2o - rasishi o3o5/4o5/2x - sishi ``` ```x3o5/4o5/3o - fix o3x5/4o5/3o - rofix o3o5/4x5/3o - rasishi o3o5/4o5/3x - sishi ``` ```x3/2o5/4o5/2o - fix o3/2x5/4o5/2o - rofix o3/2o5/4x5/2o - rasishi o3/2o5/4o5/2x - sishi ``` ```x3/2o5/4o5/3o - fix o3/2x5/4o5/3o - rofix o3/2o5/4x5/3o - rasishi o3/2o5/4o5/3x - sishi ``` otherWythoffians ```x3x5/4o5/2o - tiffix x3o5/4x5/2o - (contains gicdatrid) x3o5/4o5/2x - sishi+paphicki+gridaphi (?) o3x5/4x5/2o - [Grünbaumian] o3x5/4o5/2x - (contains cadditradid) o3o5/4x5/2x - [Grünbaumian] x3x5/4x5/2o - [Grünbaumian] x3x5/4o5/2x - (contains cadditradid) x3o5/4x5/2x - [Grünbaumian] o3x5/4x5/2x - [Grünbaumian] x3x5/4x5/2x - [Grünbaumian] ``` ```x3x5/4o5/3o - tiffix x3o5/4x5/3o - (contains gicdatrid) x3o5/4o5/3x - padohi o3x5/4x5/3o - [Grünbaumian] o3x5/4o5/3x - sirsashi o3o5/4x5/3x - quit sishi x3x5/4x5/3o - [Grünbaumian] x3x5/4o5/3x - pirshi x3o5/4x5/3x - (contains gicdatrid) o3x5/4x5/3x - [Grünbaumian] x3x5/4x5/3x - [Grünbaumian] ``` ```x3/2x5/4o5/2o - [Grünbaumian] x3/2o5/4x5/2o - sirfix x3/2o5/4o5/2x - padohi o3/2x5/4x5/2o - [Grünbaumian] o3/2x5/4o5/2x - (contains cadditradid) o3/2o5/4x5/2x - [Grünbaumian] x3/2x5/4x5/2o - [Grünbaumian] x3/2x5/4o5/2x - [Grünbaumian] x3/2o5/4x5/2x - [Grünbaumian] o3/2x5/4x5/2x - [Grünbaumian] x3/2x5/4x5/2x - [Grünbaumian] ``` ```x3/2x5/4o5/3o - [Grünbaumian] x3/2o5/4x5/3o - sirfix x3/2o5/4o5/3x - sishi+paphicki+gridaphi (?) o3/2x5/4x5/3o - [Grünbaumian] o3/2x5/4o5/3x - sirsashi o3/2o5/4x5/3x - quit sishi x3/2x5/4x5/3o - [Grünbaumian] x3/2x5/4o5/3x - [Grünbaumian] x3/2o5/4x5/3x - quippirfix o3/2x5/4x5/3x - [Grünbaumian] x3/2x5/4x5/3x - [Grünbaumian] ``` (partial)snubs andholosnubs ```... ``` ```... ``` ```... ``` ```... ```

### Hecatonicosachoral ("hyic") Symmetries – type o3o5/2o5o   (up)

 o3o5/2o5o (µ=76) o3/2o5/2o5o (µ=284) o3o5/3o5o (µ=436) o3/2o5/3o5o (µ=644) quasiregulars ```x3o5/2o5o - gofix o3x5/2o5o - rigfix o3o5/2x5o - ragaghi o3o5/2o5x - gaghi ``` ```x3/2o5/2o5o - gofix o3/2x5/2o5o - rigfix o3/2o5/2x5o - ragaghi o3/2o5/2o5x - gaghi ``` ```x3o5/3o5o - gofix o3x5/3o5o - rigfix o3o5/3x5o - ragaghi o3o5/3o5x - gaghi ``` ```x3/2o5/3o5o - gofix o3/2x5/3o5o - rigfix o3/2o5/3x5o - ragaghi o3/2o5/3o5x - gaghi ``` otherWythoffians ```x3x5/2o5o - tigfix x3o5/2x5o - (contains sicdatrid) x3o5/2o5x - quipdohi o3x5/2x5o - [Grünbaumian] o3x5/2o5x - sirgaghi o3o5/2x5x - tigaghi x3x5/2x5o - [Grünbaumian] x3x5/2o5x - pirgaghi x3o5/2x5x - (contains sicdatrid) o3x5/2x5x - [Grünbaumian] x3x5/2x5x - [Grünbaumian] ``` ```x3/2x5/2o5o - [Grünbaumian] x3/2o5/2x5o - querfix x3/2o5/2o5x - gaghi+paphacki+sridaphi (?) o3/2x5/2x5o - [Grünbaumian] o3/2x5/2o5x - sirgaghi o3/2o5/2x5x - tigaghi x3/2x5/2x5o - [Grünbaumian] x3/2x5/2o5x - [Grünbaumian] x3/2o5/2x5x - paqrigafix o3/2x5/2x5x - [Grünbaumian] x3/2x5/2x5x - [Grünbaumian] ``` ```x3x5/3o5o - tigfix x3o5/3x5o - querfix x3o5/3o5x - gaghi+paphacki+sridaphi (?) o3x5/3x5o - ghihi o3x5/3o5x - (contains cadditradid) o3o5/3x5x - tigaghi x3x5/3x5o - gaqrigafix x3x5/3o5x - (contains cadditradid) x3o5/3x5x - paqrigafix o3x5/3x5x - gaqrigaghi x3x5/3x5x - gaquidipdy ``` ```x3/2x5/3o5o - [Grünbaumian] x3/2o5/3x5o - (contains sicdatrid) x3/2o5/3o5x - quipdohi o3/2x5/3x5o - ghihi o3/2x5/3o5x - (contains cadditradid) o3/2o5/3x5x - tigaghi x3/2x5/3x5o - [Grünbaumian] x3/2x5/3o5x - [Grünbaumian] x3/2o5/3x5x - (contains sicdatrid) o3/2x5/3x5x - gaqrigaghi x3/2x5/3x5x - [Grünbaumian] ``` (partial)snubs andholosnubs ```... ``` ```... ``` ```... ``` ```... ``` o3o5/2o5/4o (µ=764) o3o5/3o5/4o (µ=1124) o3/2o5/2o5/4o (µ=1756) o3/2o5/3o5/4o (µ=2116) quasiregulars ```x3o5/2o5/4o - gofix o3x5/2o5/4o - rigfix o3o5/2x5/4o - ragaghi o3o5/2o5/4x - gaghi ``` ```x3o5/3o5/4o - gofix o3x5/3o5/4o - rigfix o3o5/3x5/4o - ragaghi o3o5/3o5/4x - gaghi ``` ```x3/2o5/2o5/4o - gofix o3/2x5/2o5/4o - rigfix o3/2o5/2x5/4o - ragaghi o3/2o5/2o5/4x - gaghi ``` ```x3/2o5/3o5/4o - gofix o3/2x5/3o5/4o - rigfix o3/2o5/3x5/4o - ragaghi o3/2o5/3o5/4x - gaghi ``` otherWythoffians ```x3x5/2o5/4o - tigfix x3o5/2x5/4o - (contains sicdatrid) x3o5/2o5/4x - gaghi+paphacki+sridaphi (?) o3x5/2x5/4o - [Grünbaumian] o3x5/2o5/4x - (contains cadditradid) o3o5/2x5/4x - [Grünbaumian] x3x5/2x5/4o - [Grünbaumian] x3x5/2o5/4x - (contains cadditradid) x3o5/2x5/4x - [Grünbaumian] o3x5/2x5/4x - [Grünbaumian] x3x5/2x5/4x - [Grünbaumian] ``` ```x3x5/3o5/4o - tigfix x3o5/3x5/4o - querfix x3o5/3o5/4x - quipdohi o3x5/3x5/4o - ghihi o3x5/3o5/4x - sirgaghi o3o5/3x5/4x - [Grünbaumian] x3x5/3x5/4o - gaqrigafix x3x5/3o5/4x - pirgaghi x3o5/3x5/4x - [Grünbaumian] o3x5/3x5/4x - [Grünbaumian] x3x5/3x5/4x - [Grünbaumian] ``` ```x3/2x5/2o5/4o - [Grünbaumian] x3/2o5/2x5/4o - querfix x3/2o5/2o5/4x - quipdohi o3/2x5/2x5/4o - [Grünbaumian] o3/2x5/2o5/4x - (contains cadditradid) o3/2o5/2x5/4x - [Grünbaumian] x3/2x5/2x5/4o - [Grünbaumian] x3/2x5/2o5/4x - [Grünbaumian] x3/2o5/2x5/4x - [Grünbaumian] o3/2x5/2x5/4x - [Grünbaumian] x3/2x5/2x5/4x - [Grünbaumian] ``` ```x3/2x5/3o5/4o - [Grünbaumian] x3/2o5/3x5/4o - (contains sicdatrid) x3/2o5/3o5/4x - gaghi+paphacki+sridaphi (?) o3/2x5/3x5/4o - ghihi o3/2x5/3o5/4x - sirgaghi o3/2o5/3x5/4x - [Grünbaumian] x3/2x5/3x5/4o - [Grünbaumian] x3/2x5/3o5/4x - [Grünbaumian] x3/2o5/3x5/4x - [Grünbaumian] o3/2x5/3x5/4x - [Grünbaumian] x3/2x5/3x5/4x - [Grünbaumian] ``` (partial)snubs andholosnubs ```... ``` ```... ``` ```... ``` ```... ```

### Hecatonicosachoral ("hyic") Symmetries – type o5o3o5/2o   (up)

 o5o3o5/2o (µ=20) o5o3o5/3o (µ=100) o5o3/2o5/2o (µ=620) o5o3/2o5/3o (µ=700) quasiregulars ```x5o3o5/2o - gahi o5x3o5/2o - raghi o5o3x5/2o - ragishi o5o3o5/2x - gishi ``` ```x5o3o5/3o - gahi o5x3o5/3o - raghi o5o3x5/3o - ragishi o5o3o5/3x - gishi ``` ```x5o3/2o5/2o - gahi o5x3/2o5/2o - raghi o5o3/2x5/2o - ragishi o5o3/2o5/2x - gishi ``` ```x5o3/2o5/3o - gahi o5x3/2o5/3o - raghi o5o3/2x5/3o - ragishi o5o3/2o5/3x - gishi ``` otherWythoffians ```x5x3o5/2o - taghi x5o3x5/2o - sraghi x5o3o5/2x - siddapady o5x3x5/2o - dahi o5x3o5/2x - (contains sicdatrid) o5o3x5/2x - [Grünbaumian] x5x3x5/2o - graghi x5x3o5/2x - (contains sicdatrid) x5o3x5/2x - [Grünbaumian] o5x3x5/2x - [Grünbaumian] x5x3x5/2x - [Grünbaumian] ``` ```x5x3o5/3o - taghi x5o3x5/3o - sraghi x5o3o5/3x - quadippady o5x3x5/3o - dahi o5x3o5/3x - qraghi o5o3x5/3x - quit gishi x5x3x5/3o - graghi x5x3o5/3x - paqraghi x5o3x5/3x - quippirghi o5x3x5/3x - gaqrigashi x5x3x5/3x - gaquidphihi ``` ```x5x3/2o5/2o - taghi x5o3/2x5/2o - (contains gicdatrid) x5o3/2o5/2x - quadippady o5x3/2x5/2o - [Grünbaumian] o5x3/2o5/2x - qraghi o5o3/2x5/2x - [Grünbaumian] x5x3/2x5/2o - [Grünbaumian] x5x3/2o5/2x - paqraghi x5o3/2x5/2x - [Grünbaumian] o5x3/2x5/2x - [Grünbaumian] x5x3/2x5/2x - [Grünbaumian] ``` ```x5x3/2o5/3o - taghi x5o3/2x5/3o - (contains gicdatrid) x5o3/2o5/3x - siddapady o5x3/2x5/3o - [Grünbaumian] o5x3/2o5/3x - (contains sicdatrid) o5o3/2x5/3x - quit gishi x5x3/2x5/3o - [Grünbaumian] x5x3/2o5/3x - (contains sicdatrid) x5o3/2x5/3x - (contains gicdatrid) o5x3/2x5/3x - [Grünbaumian] x5x3/2x5/3x - [Grünbaumian] ``` (partial)snubs andholosnubs ```... ``` ```... ``` ```... ``` ```... ``` o5/4o3o5/2o (µ=820) o5/4o3/2o5/2o (µ=1420) o5/4o3o5/3o (µ=1460) o5/4o3/2o5/3o (µ=2060) quasiregulars ```x5/4o3o5/2o - gahi o5/4x3o5/2o - raghi o5/4o3x5/2o - ragishi o5/4o3o5/2x - gishi ``` ```x5/4o3/2o5/2o - gahi o5/4x3/2o5/2o - raghi o5/4o3/2x5/2o - ragishi o5/4o3/2o5/2x - gishi ``` ```x5/4o3o5/3o - gahi o5/4x3o5/3o - raghi o5/4o3x5/3o - ragishi o5/4o3o5/3x - gishi ``` ```x5/4o3/2o5/3o - gahi o5/4x3/2o5/3o - raghi o5/4o3/2x5/3o - ragishi o5/4o3/2o5/3x - gishi ``` otherWythoffians ```x5/4x3o5/2o - [Grünbaumian] x5/4o3x5/2o - (contains gicdatrid) x5/4o3o5/2x - quadippady o5/4x3x5/2o - dahi o5/4x3o5/2x - (contains sicdatrid) o5/4o3x5/2x - [Grünbaumian] x5/4x3x5/2o - [Grünbaumian] x5/4x3o5/2x - [Grünbaumian] x5/4o3x5/2x - [Grünbaumian] o5/4x3x5/2x - [Grünbaumian] x5/4x3x5/2x - [Grünbaumian] ``` ```x5/4x3/2o5/2o - [Grünbaumian] x5/4o3/2x5/2o - sraghi x5/4o3/2o5/2x - siddapady o5/4x3/2x5/2o - [Grünbaumian] o5/4x3/2o5/2x - qraghi o5/4o3/2x5/2x - [Grünbaumian] x5/4x3/2x5/2o - [Grünbaumian] x5/4x3/2o5/2x - [Grünbaumian] x5/4o3/2x5/2x - [Grünbaumian] o5/4x3/2x5/2x - [Grünbaumian] x5/4x3/2x5/2x - [Grünbaumian] ``` ```x5/4x3o5/3o - [Grünbaumian] x5/4o3x5/3o - (contains gicdatrid) x5/4o3o5/3x - siddapady o5/4x3x5/3o - dahi o5/4x3o5/3x - qraghi o5/4o3x5/3x - quit gishi x5/4x3x5/3o - [Grünbaumian] x5/4x3o5/3x - [Grünbaumian] x5/4o3x5/3x - (contains gicdatrid) o5/4x3x5/3x - gaqrigashi x5/4x3x5/3x - [Grünbaumian] ``` ```x5/4x3/2o5/3o - [Grünbaumian] x5/4o3/2x5/3o - sraghi x5/4o3/2o5/3x - quadippady o5/4x3/2x5/3o - [Grünbaumian] o5/4x3/2o5/3x - (contains sicdatrid) o5/4o3/2x5/3x - quit gishi x5/4x3/2x5/3o - [Grünbaumian] x5/4x3/2o5/3x - [Grünbaumian] x5/4o3/2x5/3x - quippirghi o5/4x3/2x5/3x - [Grünbaumian] x5/4x3/2x5/3x - [Grünbaumian] ``` (partial)snubs andholosnubs ```... ``` ```... ``` ```... ``` ```... ```

### Hecatonicosachoral ("hyic") Symmetries – type o5o5/2o5o   (up)

 o5o5/2o5o (µ=6) o5o5/2o5/4o (µ=354) o5o5/3o5o (µ=366) quasiregulars ```x5o5/2o5o - gohi o5x5/2o5o - righi ``` ```x5o5/2o5/4o - gohi o5x5/2o5/4o - righi o5o5/2x5/4o - righi o5o5/2o5/4x - gohi ``` ```x5o5/3o5o - gohi o5x5/3o5o - righi ``` otherWythoffians ```x5x5/2o5o - tighi x5o5/2x5o - sirghi x5o5/2o5x - 2sophi (?) o5x5/2x5o - [Grünbaumian] x5x5/2x5o - [Grünbaumian] x5x5/2o5x - pirghi x5x5/2x5x - [Grünbaumian] ``` ```x5x5/2o5/4o - tighi x5o5/2x5/4o - sirghi x5o5/2o5/4x - 2gaghi+2paphacki (?) o5x5/2x5/4o - [Grünbaumian] o5x5/2o5/4x - (contains cadditradid) o5o5/2x5/4x - [Grünbaumian] x5x5/2x5/4o - [Grünbaumian] x5x5/2o5/4x - (contains cadditradid) x5o5/2x5/4x - [Grünbaumian] o5x5/2x5/4x - [Grünbaumian] x5x5/2x5/4x - [Grünbaumian] ``` ```x5x5/3o5o - tighi x5o5/3x5o - (contains cadditradid) x5o5/3o5x - 2gaghi+2paphacki (?) o5x5/3x5o - 2gitphi x5x5/3x5o - sabbadipady+sanbathi (?) x5x5/3o5x - (contains cadditradid) x5x5/3x5x - 2gidditpix+2dithix (?) ``` (partial)snubs andholosnubs ```... ``` ```... ``` ```... ``` o5o5/3o5/4o (µ=714) o5/4o5/2o5/4o (µ=2166) o5/4o5/3o5/4o (µ=2526) quasiregulars ```x5o5/3o5/4o - gohi o5x5/3o5/4o - righi o5o5/3x5/4o - righi o5o5/3o5/4x - gohi ``` ```x5/4o5/2o5/4o - gohi o5/4x5/2o5/4o - righi ``` ```x5/4o5/3o5/4o - gohi o5/4x5/3o5/4o - righi ``` otherWythoffians ```x5x5/3o5/4o - tighi x5o5/3x5/4o - (contains cadditradid) x5o5/3o5/4x - 2sophi (?) o5x5/3x5/4o - 2gitphi (?) o5x5/3o5/4x - sirghi o5o5/3x5/4x - [Grünbaumian] x5x5/3x5/4o - sabbadipady+sanbathi (?) x5x5/3o5/4x - pirghi x5o5/3x5/4x - [Grünbaumian] o5x5/3x5/4x - [Grünbaumian] x5x5/3x5/4x - [Grünbaumian] ``` ```x5/4x5/2o5/4o - [Grünbaumian] x5/4o5/2x5/4o - (contains cadditradid) x5/4o5/2o5/4x - 2sophi (?) o5/4x5/2x5/4o - [Grünbaumian] x5/4x5/2x5/4o - [Grünbaumian] x5/4x5/2o5/4x - [Grünbaumian] x5/4x5/2x5/4x - [Grünbaumian] ``` ```x5/4x5/3o5/4o - [Grünbaumian] x5/4o5/3x5/4o - sirghi x5/4o5/3o5/4x - 2gaghi+2paphacki (?) o5/4x5/3x5/4o - 2gitphi (?) x5/4x5/3x5/4o - [Grünbaumian] x5/4x5/3o5/4x - [Grünbaumian] x5/4x5/3x5/4x - [Grünbaumian] ``` (partial)snubs andholosnubs ```... ``` ```... ``` ```... ```

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

 o5/2o5o5/2o (µ=66) o5/2o5o5/3o (µ=294) o5/3o5o5/3o (µ=786) quasiregulars ```x5/2o5o5/2o - gashi o5/2x5o5/2o - ragashi ``` ```x5/2o5o5/3o - gashi o5/2x5o5/3o - ragashi o5/2o5x5/3o - ragashi o5/2o5o5/3x - gashi ``` ```x5/3o5o5/3o - gashi o5/3x5o5/3o - ragashi ``` otherWythoffians ```x5/2x5o5/2o - [Grünbaumian] x5/2o5x5/2o - sirgashi x5/2o5o5/2x - 2sishi+2paphicki (?) o5/2x5x5/2o - 2sitphi (?) x5/2x5x5/2o - [Grünbaumian] x5/2x5o5/2x - [Grünbaumian] x5/2x5x5/2x - [Grünbaumian] ``` ```x5/2x5o5/3o - [Grünbaumian] x5/2o5x5/3o - sirgashi x5/2o5o5/3x - 2quiphi (?) o5/2x5x5/3o - 2sitphi (?) o5/2x5o5/3x - (contains cadditradid) o5/2o5x5/3x - quit gashi x5/2x5x5/3o - [Grünbaumian] x5/2x5o5/3x - [Grünbaumian] x5/2o5x5/3x - quippirgashi o5/2x5x5/3x - gabbadipady+ganbathi (?) x5/2x5x5/3x - [Grünbaumian] ``` ```x5/3x5o5/3o - quit gashi x5/3o5x5/3o - (contains cadditradid) x5/3o5o5/3x - 2sishi+2paphicki (?) o5/3x5x5/3o - 2sitphi (?) x5/3x5x5/3o - gabbadipady+ganbathi (?) x5/3x5o5/3x - (contains cadditradid) x5/3x5x5/3x - 2sidditpix+2dithix (?) ``` (partial)snubs andholosnubs ```... ``` ```... ``` ```... ``` o5/2o5/4o5/2o (µ=1146) o5/2o5/4o5/3o (µ=1374) o5/3o5/4o5/3o (µ=1866) quasiregulars ```x5/2o5/4o5/2o - gashi o5/2x5/4o5/2o - ragashi ``` ```x5/2o5/4o5/3o - gashi o5/2x5/4o5/3o - ragashi o5/2o5/4x5/3o - ragashi o5/2o5/4o5/3x - gashi ``` ```x5/3o5/4o5/3o - gashi o5/3x5/4o5/3o - ragashi ``` otherWythoffians ```x5/2x5/4o5/2o - [Grünbaumian] x5/2o5/4x5/2o - (contains cadditradid) x5/2o5/4o5/2x - 2quiphi (?) o5/2x5/4x5/2o - [Grünbaumian] x5/2x5/4x5/2o - [Grünbaumian] x5/2x5/4o5/2x - [Grünbaumian] x5/2x5/4x5/2x - [Grünbaumian] ``` ```x5/2x5/4o5/3o - [Grünbaumian] x5/2o5/4x5/3o - (contains cadditradid) x5/2o5/4o5/3x - 2sishi+2paphicki (?) o5/2x5/4x5/3o - [Grünbaumian] o5/2x5/4o5/3x - sirgashi o5/2o5/4x5/3x - quit gashi x5/2x5/4x5/3o - [Grünbaumian] x5/2x5/4o5/3x - [Grünbaumian] x5/2o5/4x5/3x - (contains cadditradid) o5/2x5/4x5/3x - [Grünbaumian] x5/2x5/4x5/3x - [Grünbaumian] ``` ```x5/3x5/4o5/3o - quit gashi x5/3o5/4x5/3o - sirgashi x5/3o5/4o5/3x - 2quiphi (?) o5/3x5/4x5/3o - [Grünbaumian] x5/3x5/4x5/3o - [Grünbaumian] x5/3x5/4o5/3x - quippirgashi x5/3x5/4x5/3x - [Grünbaumian] ``` (partial)snubs andholosnubs ```... ``` ```... ``` ```... ```

 tridental ones ```o-P-o-Q-o *b-R-o = o_ -P_ >o---R---o _Q- o- ```

### Demitesseractic ("demitessic") Symmetries   (up)

 o3o3o *b3o (convex) o3o3o *b3/2o (µ=7) o3/2o3/2o *b3o (µ=17) o3/2o3/2o *b3/2o (µ=23) quasiregulars ```x3o3o *b3o - hex o3x3o *b3o - ico ``` ```x3o3o *b3/2o - hex o3x3o *b3/2o - ico o3o3o *b3/2x - hex ``` ```x3/2o3/2o *b3o - hex o3/2x3/2o *b3o - ico o3/2o3/2o *b3x - hex ``` ```x3/2o3/2o *b3/2o - hex o3/2x3/2o *b3/2o - ico ``` otherWythoffians ```x3x3o *b3o - thex x3o3x *b3o - rit x3x3x *b3o - tah x3o3x *b3x - rico x3x3x *b3x - tico ``` ```x3x3o *b3/2o - thex x3o3x *b3/2o - rit x3o3o *b3/2x - 2tho+24{4} (?) o3x3o *b3/2x - [Grünbaumian] x3x3x *b3/2o - tah x3x3o *b3/2x - [Grünbaumian] x3o3x *b3/2x - gico+8co+16 2thah (?) x3x3x *b3/2x - [Grünbaumian] ``` ```x3/2x3/2o *b3o - [Grünbaumian] x3/2o3/2x *b3o - rit x3/2o3/2o *b3x - 2tho+24{4} (?) o3/2x3/2o *b3x - thex x3/2x3/2x *b3o - [Grünbaumian] x3/2x3/2o *b3x - [Grünbaumian] x3/2o3/2x *b3x - gico+8co+16 2thah (?) x3/2x3/2x *b3x - [Grünbaumian] ``` ```x3/2x3/2o *b3/2o - [Grünbaumian] x3/2o3/2x *b3/2o - rit x3/2x3/2x *b3/2o - [Grünbaumian] x3/2o3/2x *b3/2x - rico x3/2x3/2x *b3/2x - [Grünbaumian] ``` (partial)snubs andholosnubs ```β3o3o *b3o - 2hex+8oct (?) o3β3o *b3o - ico+gico+72{4} (?) β3x3o *b3o - 2ico (?) x3β3o *b3o - (?) *) β3β3o *b3o - 2ico+48{4}+128{3} (?) **) β3o3x *b3o - sto+16tet (?) β3o3β *b3o - (?) *) β3x3x *b3o - 2thex (?) x3β3x *b3o - (?) *) β3β3x *b3o - (?) *) β3x3β *b3o - (?) *) β3β3β *b3o - (?) *) β3o3x *b3x - rawvhitto β3o3β *b3x - (?) *) β3o3β *b3β - (?) *) β3x3x *b3x - 2tah (?) x3β3x *b3x - 2rico (?) β3β3x *b3x - 2rico (?) β3x3β *b3x - (?) *) β3β3β *b3x - (?) *) β3x3β *b3β - (?) *) s3s3s *b3s - sadi ``` ```... ``` ```... ``` ```s3/2s3/2s *b3/2s - rasdi ... ```

### Tetrahedral Prism Symmetries   (up)

 o o3o3o (convex) o o3/2o3o3*b (µ=2) o o3/2o3o (µ=3) quasiregularcomponents ```x x3o3o - tepe x o3x3o - ope ``` ```x x3/2o3o3*b - (contains "2tet") x o3/2o3x3*b - (contains "2tet") ``` ```x x3/2o3o - tepe x o3/2x3o - ope x o3/2o3x - tepe ``` otherWythoffians ```x x3x3o - tuttip x x3o3x - cope x x3x3x - tope ``` ```x x3/2x3o3*b - (contains "2oct") x x3/2o3x3*b - ohope x x3/2x3x3*b - (contains "2tut") ``` ```x x3/2x3o - (contains "3tet") x x3/2o3x - 2thahp (?) x o3/2x3x - tuttip x x3/2x3x - (contains "cho+4{6/2}") ``` (partial)snubs andholosnubs ```x2s3s3s - ipe x s3s3s - ipe ... ``` ```... ``` ```... ``` o o3/2o3/2o (µ=5) o o3/2o3/2o3/2*b (µ=6) quasiregularcomponents ```x x3/2o3/2o - tepe x o3/2x3/2o - ope ``` ```x x3/2o3/2o3/2*b - (contains "2tet") ``` otherWythoffians ```x x3/2x3/2o - (contains "3tet") x x3/2o3/2x - cope x x3/2x3/2x - (contains "2oct+6{4}") ``` ```x x3/2x3/2o3/2*b - (contains "2oct") x x3/2x3/2x3/2*b - (contains "6tet") ``` (partial)snubs andholosnubs ```x s3/2s3/2s - gipe ... ``` ```... ```

### Octahedral Prism Symmetries   (up)

 o o3o4o (convex) o o3/2o4o4*b (µ=2) o o4/3o3o4*b (µ=4) o o3/2o4o (µ=5) quasiregularcomponents ```x x3o4o - ope x o3x4o - cope x o3o4x - tes ``` ```x x3/2o4o4*b - (contains "oct+6{4}") x o3/2o4x4*b - (contains "2cube") ``` ```x x4/3o3o4*b - (contains "2cube") x o4/3x3o4*b - (contains "oct+6{4}") x o4/3o3x4*b - (contains "oct+6{4}") ``` ```x x3/2o4o - ope x o3/2x4o - cope x o3/2o4x - tes ``` otherWythoffians ```x x3x4o - tope x x3o4x - sircope x o3x4x - ticcup x x3x4x - gircope ``` ```x x3/2x4o4*b - (contains "2co") x x3/2o4x4*b - soccope x x3/2x4x4*b - (contains "2tic") ``` ```x x4/3x3o4*b - goccope x x4/3o3x4*b - soccope x o4/3x3x4*b - (contains "2cho") x x4/3x3x4*b - cotcope ``` ```x x3/2x4o - (contains "2oct+6{4}") x x3/2o4x - quercope x o3/2x4x - ticcup x x3/2x4x - (contains "sroh+8{6/2}") ``` (partial)snubs andholosnubs ```x2o3o4s - tepe x o3o4s - tepe s2o3o4s - hex x2s3s4o - ipe x s3s4o - ipe s2x3o4s - tutcup x2s3s4x - sircope x s3s4x - sircope x s3s4s - sniccup ... ``` ```... ``` ```... ``` ```x s3/2s4o - gipe ... ``` o o4/3o3o (µ=7) o o4/3o3/2o (µ=11) o o4/3o4/3o3/2*a (µ=14) quasiregularcomponents ```x x4/3o3o - tes x o4/3x3o - cope x o4/3o3x - ope ``` ```x x4/3o3/2o - tes x o4/3x3/2o - cope x o4/3o3/2x - ope ``` ```x x4/3o4/3o3/2*b - (contains "oct+6{4}") x o4/3x4/3o3/2*b - (contains "2cube") ``` otherWythoffians ```x x4/3x3o - quithip x x4/3o3x - quercope x o4/3x3x - tope x x4/3x3x - quitcope ``` ```x x4/3x3/2o - quithip x x4/3o3/2x - sircope x o4/3x3/2x - (contains "2oct+6{4}") x x4/3x3/2x - (contains "groh+8{6/2}") ``` ```x x4/3x4/3o3/2*b - goccope x x4/3o4/3x3/2*b - (contains "2co") x x4/3x4/3x3/2*b - (contains "2quith") ``` (partial)snubs andholosnubs ```x o4/3s3s - ipe ... ``` ```x o4/3s3/2s - gipe ... ``` ```... ```

### Icosahedral Prism Symmetries   (up)

 o o3o5o (convex) o o5/2o3o3*b (µ=2) o o3/2o5o5*b (µ=2) quasiregularcomponents ```x x3o5o - ipe x o3x5o - iddip x o3o5x - dope ``` ```x x5/2o3o3*b - sidtiddip x o5/2o3x3*b - (contains "2ike") ``` ```x x3/2o5o5*b - (contains cid) x o3/2o5x5*b - (contains "2doe") ``` otherWythoffians ```x x3x5o - tipe x x3o5x - sriddip x o3x5x - tiddip x x3x5x - griddip ``` ```x x5/2x3o3*b - (contains "2id") x x5/2o3x3*b - siidip x x5/2x3x3*b - (contains "2ti") ``` ```x x3/2x5o5*b - (contains "2id") x x3/2o5x5*b - saddiddip x x3/2x5x5*b - (contains "2tid") ``` (partial)snubs andholosnubs ```x s3s5s - sniddip β2o3o5β - sidtidap ... ``` ```x s5/2s3s3*a - sesidip ... ``` ```... ``` o o5/2o5o (µ=3) o o5/3o3o5*b (µ=4) o o5/2o5/2o5/2*b (µ=6) quasiregularcomponents ```x x5/2o5o - sissiddip x o5/2x5o - diddip x o5/2o5x - gaddip ``` ```x x5/3o3o5*b - ditdiddip x o5/3x3o5*b - (contains gacid) x o5/3o3x5*b - (contains cid) ``` ```x x5/2o5/2o5/2*b - (contains "2sissid") ``` otherWythoffians ```x x5/2x5o - (contains "3doe") x x5/2o5x - radiddip x o5/2x5x - tigiddip x x5/2x5x - (contains "sird+12{10/2}") ``` ```x x5/3x3o5*b - gidditdiddip x x5/3o3x5*b - sidditdiddip x o5/3x3x5*b - ididdip x x5/3x3x5*b - idtiddip ``` ```x x5/2x5/2o5/2*b - (contains "2did") x x5/2x5/2x5/2*b - (contains "6doe") ``` (partial)snubs andholosnubs ```x s5/2s5s - siddiddip ... ``` ```x s5/3s3s5*b - sididdip ... ``` ```... ``` o o3/2o3o5*b (µ=6) o o5/4o5o5*b (µ=6) o o5/2o3o (µ=7) quasiregularcomponents ```x x3/2o3o5*b - gidtiddip x o3/2x3o5*b - (contains "2gike") x o3/2o3x5*b - gidtiddip ``` ```x x5/4o5o5*b - (contains "2gad") x o5/4o5x5*b - (contains "2gad") ``` ```x x5/2o3o - gissiddip x o5/2x3o - giddip x o5/2o3x - gipe ``` otherWythoffians ```x x3/2x3o5*b - (contains "3ike+gad") x x3/2o3x5*b - (contains "2seihid") x o3/2x3x5*b - giidip x x3/2x3x5*b - (contains "siddy+20{6/2}") ``` ```x x5/4x5o5*b - (contains "2did") x x5/4o5x5*b - (contains "2sidhid") x x5/4x5x5*b - (contains "2tigid") ``` ```x x5/2x3o - (contains "2gad+ike") x x5/2o3x - (contains sicdatrid) x o5/2x3x - tiggipe x x5/2x3x - (contains "ri+12{10/2}") ``` (partial)snubs andholosnubs ```... ``` ```... ``` ```x s5/2s3s - gosiddip β2β5/2o3o - gidtidap ... ``` o o3/2o5/2o5*b (µ=8) o o5/3o5o (µ=9) o o5/4o3o5*b (µ=10) quasiregularcomponents ```x x3/2o5/2o5*b - (contains cid) x o3/2x5/2o5*b - (contains gacid) x o3/2o5/2x5*b - ditdiddip ``` ```x x5/3o5o - sissiddip x o5/3x5o - diddip x o5/3o5x - gaddip ``` ```x x5/4o3o5*b - (contains "2doe") x o5/4x3o5*b - (contains cid) x o5/4o3x5*b - (contains cid) ``` otherWythoffians ```x x3/2x5/2o5*b - (contains "sidtid+gidtid") x x3/2o5/2x5*b - sidditdiddip x o3/2x5/2x5*b - (contains "ike+3gad") x x3/2x5/2x5*b - (contains "id+seihid+sidhid") ``` ```x x5/3x5o - quit sissiddip x x5/3o5x - (contains cadditradid) x o5/3x5x - tigiddip x x5/3x5x - quitdiddip ``` ```x x5/4x3o5*b - (contains "sidtid+ditdid") x x5/4o3x5*b - saddiddip x o5/4x3x5*b - (contains "2gidhei") x x5/4x3x5*b - (contains "siddy+12{10/4}") ``` (partial)snubs andholosnubs ```... ``` ```x s5/3s5s - isdiddip ... ``` ```... ``` o o5/3o5/2o3*b (µ=10) o o3/2o5o (µ=11) o o5/3o3o (µ=13) quasiregularcomponents ```x x5/3o5/2o3*b - (contains gacid) x o5/3x5/2o3*b - (contains "2gissid") x o5/3o5/2x3*b - (contains gacid) ``` ```x x3/2o5o - ipe x o3/2x5o - iddip x o3/2o5x - dope ``` ```x x5/3o3o - gissiddip x o5/3x3o - giddip x o5/3o3x - gipe ``` otherWythoffians ```x x5/3x5/2o3*b - gaddiddip x x5/3o5/2x3*b - (contains "2sidhei") x o5/3x5/2x3*b - (contains "ditdid+gidtid") x x5/3x5/2x3*b - (contains "giddy+12{10/2}") ``` ```x x3/2x5o - (contains "2ike+gad") x x3/2o5x - (contains gicdatrid) x o3/2x5x - tiddip x x3/2x5x - (contains "sird+20{6/2}") ``` ```x x5/3x3o - quit gissiddip x x5/3o3x - qriddip x o5/3x3x - tiggipe x x5/3x3x - gaquatiddip ``` (partial)snubs andholosnubs ```x s5/3s5/2s3*b - gisdiddip ... ``` ```... ``` ```x s5/3s3s - gisiddip ... ``` o o5/4o3o3*b (µ=14) o o3/2o5/2o5/2*b (µ=14) o o5/4o5/2o3*b (µ=16) quasiregularcomponents ```x x5/4o3o3*b - gidtiddip x o5/4o3x3*b - (contains "2gike") ``` ```x x3/2o5/2o5/2*b - (contains gacid) x o3/2o5/2x5/2*b - (contains "2gissid") ``` ```x x5/4o5/2o3*b - (contains cid) x o5/4x5/2o3*b - ditdiddip x o5/4o5/2x3*b - (contains gacid) ``` otherWythoffians ```x x5/4x3o3*b - (contains "2gid") x x5/4o3x3*b - giidip x x5/4x3x3*b - (contains "2tiggy") ``` ```x x3/2x5/2o5/2*b - (contains "2gid") x x3/2o5/2x5/2*b - (contains "ditdid+gidtid") x x3/2x5/2x5/2*b - (contains "2ike+4gad") ``` ```x x5/4x5/2o3*b - (contains "3sissid+gike") x x5/4o5/2x3*b - ididdip x o5/4x5/2x3*b - (contains "ike+3gad") x x5/4x5/2x3*b - (contains "did+sidhei+gidhei") ``` (partial)snubs andholosnubs ```... ``` ```... ``` ```... ``` o o3/2o5/2o (µ=17) o o3/2o5/3o3*b (µ=18) o o5/3o5/3o5/2*b (µ=18) quasiregularcomponents ```x x3/2o5/2o - gipe x o3/2x5/2o - giddip x o3/2o5/2x - gissiddip ``` ```x x3/2o5/3o3*b - (contains "2ike") x o3/2x5/3o3*b - sidtiddip x o3/2o5/3x3*b - sidtiddip ``` ```x x5/3o5/3o5/2*b - (contains "2sissid") x o5/3x5/3o5/2*b - (contains "2sissid") ``` otherWythoffians ```x x3/2x5/2o - (contains "2gike+sissid") x x3/2o5/2x - qriddip x o3/2x5/2x - (contains "2gad+ike") x x3/2x5/2x - (contains "2gidtid+5cube") ``` ```x x3/2x5/3o3*b - (contains "sissid+3gike") x x3/2o5/3x3*b - siidip x o3/2x5/3x3*b - (contains "2geihid") x x3/2x5/3x3*b - (contains "giddy+20{6/2}") ``` ```x x5/3x5/3o5/2*b - (contains "2gidhid") x x5/3o5/3x5/2*b - (contains "2did") x x5/3x5/3x5/2*b - (contains "2quitsissid") ``` (partial)snubs andholosnubs ```... ``` ```... ``` ```... ``` o o5/4o3o (µ=19) o o5/4o5/2o (µ=21) o o3/2o3/2o5/2*b (µ=22) quasiregularcomponents ```x x5/4o3o - dope x o5/4x3o - iddip x o5/4o3x - ipe ``` ```x x5/4o5/2o - gaddip x o5/4x5/2o - diddip x o5/4o5/2x - sissiddip ``` ```x x3/2o3/2o5/2*b - sidtiddip x o3/2x3/2o5/2*b - (contains "2ike") ``` otherWythoffians ```x x5/4x3o - (contains "2sissid+gike") x x5/4o3x - (contains gicdatrid) x o5/4x3x - tipe x x5/4x3x - (contains "ri+12{10/4}") ``` ```x x5/4x5/2o - (contains "3gissid") x x5/4o5/2x - (contains cadditradid) x o5/4x5/2x - (contains "3doe") x x5/4x5/2x - (contains "2ditdid+5cube") ``` ```x x3/2x3/2o5/2*b - (contains "sissid+3gike") x x3/2o3/2x5/2*b - (contains "2id") x x3/2x3/2x5/2*b - (contains "4ike+2gad") ``` (partial)snubs andholosnubs ```... ``` ```... ``` ```x s3/2s3/2s5/2*b - sirsiddip ... ``` o o3/2o5/3o (µ=23) o o3/2o5/3o5/3*b (µ=26) o o5/4o5/3o (µ=27) quasiregularcomponents ```x x3/2o5/3o - gipe x o3/2x5/3o - giddip x o3/2o5/3x - gissiddip ``` ```x x3/2o5/3o5/3*b - (contains gacid) x o3/2o5/3x5/3*b - (contains "2gissid") ``` ```x x5/4o5/3o - gaddip x o5/4x5/3o - diddip x o5/4o5/3x - sissiddip ``` otherWythoffians ```x x3/2x5/3o - (contains "2gike+sissid") x x3/2o5/3x - (contains sicdatrid) x o3/2x5/3x - quit gissiddip x x3/2x5/3x - (contains "gird+20{6/2}") ``` ```x x3/2x5/3o5/3*b - (contains "2gid") x x3/2o5/3x5/3*b - gaddiddip x x3/2x5/3x5/3*b - (contains "2quitgissid") ``` ```x x5/4x5/3o - (contains "3gissid") x x5/4o5/3x - radiddip x o5/4x5/3x - quit sissiddip x x5/4x5/3x - (contains "gird+12{10/4}") ``` (partial)snubs andholosnubs ```x s3/2s5/3s - girsiddip ... ``` ```... ``` ```... ``` o o5/4o3/2o (µ=29) o o5/4o3/2o5/3*b (µ=32) o o5/4o3/2o3/2*b (µ=34) quasiregularcomponents ```x x5/4o3/2o - dope x o5/4x3/2o - iddip x o5/4o3/2x - ipe ``` ```x x5/4o3/2o5/3*b - ditdiddip x o5/4x3/2o5/3*b - (contains cid) x o5/4o3/2x5/3*b - (contains gacid) ``` ```x x5/4o3/2o3/2*b - gidtiddip x o5/4o3/2x3/2*b - (contains "2gike") ``` otherWythoffians ```x x5/4x3/2o - (contains "2sissid+gike") x x5/4o3/2x - sriddip x o5/4x3/2x - (contains "2ike+gad") x x5/4x3/2x - (contains "2sidtid+5cube") ``` ```x x5/4x3/2o5/3*b - (contains "3sissid+gike") x x5/4o3/2x5/3*b - (contains "sidtid+gidtid") x o5/4x3/2x5/3*b - gidditdiddip x x5/4x3/2x5/3*b - (contains "gid+geihid+gidhid") ``` ```x x5/4x3/2o3/2*b - (contains "2gid") x x5/4o3/2x3/2*b - (contains "3ike+gad") x x5/4x3/2x3/2*b - (contains 2sissid+4gike") ``` (partial)snubs andholosnubs ```... ``` ```... ``` ```... ``` o o5/4o5/4o3/2*b (µ=38) o o5/4o5/4o5/4*b (µ=42) quasiregularcomponents ```x x5/4o5/4o3/2*b - (contains cid) x o5/4x5/4o3/2*b - (contains "2doe") ``` ```x x5/4o5/4o5/4*b - (contains "2gad") ``` otherWythoffians ```x x5/4x5/4o3/2*b - (contains "sidtid+ditdid") x x5/4o5/4x3/2*b - (contains "2id") x x5/4x5/4x3/2*b - (contains "4sissid+2gike") ``` ```x x5/4x5/4o5/4*b - (contains "2did") x x5/4x5/4x5/4*b - (contains "6gissid") ``` (partial)snubs andholosnubs ```... ``` ```... ```

### Duoprisms & Prismatic Prisms

 o-n/d-o o-m/b-o o o o-n/d-o o o o o of quasiregulars ```x3o x3o - triddip x3o x4o - tisdip x4o x4o - tes ... x3o xno - 3,n-dip x4o xno - 4,n-dip ... xno xno - n,n-dip xno xmo - n,m-dip x-n/d-o x-m/b-o - n/d,m/b-dip ``` ```x x x3o - tisdip x x x4o - tes ... x x xno - 4,n-dip ``` ```x x x x - tes ``` otherWythoffians ```x3x x3o - thiddip x3x x3x - hiddip x3o x4x - todip x3x x4o - shiddip x3x x4x - hodip x4o x4x - sodip ... x4o xnx - 4,2n-dip x3x xno - 6,n-dip x4x xno - 8,n-dip ... xnx xmo - 2n,m-dip xnx xmx - 2n,2m-dip ``` ```x x x3x - shiddip x x x4x - sodip ... x x xnx - 4,2n-dip ``` ```  ``` (partial)snubs andholosnubs ```s3s2x3o - triddip s3s x3o - triddip s3s2x3x - thiddip s3s x3x - thiddip s4o2s4o - hex s4x s4x - tes s4x2s4x - (?) *) s5/3s2s5s - gudap ... ``` ```s2s2s4o - hex ... x s2s2no - n-appip x s-2-s-2n/d-o - n/d-appip x s2s3s - ope x s2s4s - squappip ... x s2sns - n-appip x s-2-s-n/d-s - n/d-appip x x s3s - tisdip ... x x sns - 4,n-dip ``` ```s2s2s2s - hex x s2s2s - tepe ```

### other non-kaleidoscopical uniform polychora   (up)

 acc. to other regiments making up own regiments ```affic (afdec regiment) = hemi( x3x4x3x4*a4/3*c *b4/3*d ) chope (cope regiment) dard tipady (dattady regiment) dittadphi (dattady regiment) dittafady (dattady regiment) = hemi( x5o5/3x5o5/3*a3*c ) gidard tipady (dattady regiment) grad tathi (dattady regiment) gridtathi (dattady regiment) mardatathi (dattady regiment) ridatathi (dattady regiment) gadathiphi (gadtaxady regiment) = reduced( x5/3o3x3/2o3*b , by 2tet ) gadtifady (gadtaxady regiment) = hemi( x5/2o3x5/2o3*a5/3*c ) gardatady (gadtaxady regiment) = reduced( x3/2o3o3o5/3*a5*c , by {5} ) gardatathi (gadtaxady regiment) = reduced( x5/3x5/3o3o5*a3/2*c , by gitphi ) gardtapaxhi (gadtaxady regiment) girpdo (gichado regiment) gahfipto (gittith regiment) gaquipadah (gittith regiment) gittifcoth (gittith regiment) gnappoth (gittith regiment) picnut (gittith regiment) grohp (goccope regiment) gipriphi (gwavixady regiment) = reduced( x5/3x3o3/2x , by 2thah ) tho (hex regiment) dod honho (ico regiment) doh honho (ico regiment) ghahoh (ico regiment) hodho (ico regiment) hoh honho (ico regiment) hohoh (ico regiment) huhoh (ico regiment) ihi (ico regiment) odho (ico regiment) oh (ico regiment) ohuhoh (ico regiment) ratho (ico regiment) shahoh (ico regiment) thahp (ope regiment) ripdip (prip regiment) sirpdo (prit regiment) sirpith (proh regiment) girpith (quiproh regiment) firgaghi (ragaghi regiment) mohiny (ragaghi regiment) prap vixhi (ragishi regiment) spapivady (ragishi regiment) firp (rap regiment) = hemi( x3o3o3/2x ) pinnip (rap regiment) = reduced( x3o3/2x3o , by 2thah ) fry (rahi regiment) shinhi (rahi regiment) firsashi (rasishi regiment) hinhi (rasishi regiment) frico (rico regiment) ini (rico regiment) frogfix (rigfix regiment) gippapivady (rigfix regiment) graphi (rigfix regiment) mif pixady (rigfix regiment) ofpipixhi (rigfix regiment) omfapaxady (rigfix regiment) quiphi (rigfix regiment) ripahi (rigfix regiment) = reduced( x3o3/2x5/2o , by 2thah ) giprapivady (righi regiment) papvixhi (righi regiment) firgogishi (rigogishi regiment) gohiny (rigogishi regiment) dithix (rissidtixhi regiment) gaddit thix (rissidtixhi regiment) gidditpix (rissidtixhi regiment) giddit thix (rissidtixhi regiment) gidthidy hi (rissidtixhi regiment) gotdatixhi (rissidtixhi regiment) gotditpix (rissidtixhi regiment) middit thix (rissidtixhi regiment) sidditpix (rissidtixhi regiment) siddit thix (rissidtixhi regiment) sidthidy hi (rissidtixhi regiment) stodatixhi (rissidtixhi regiment) stoditpix (rissidtixhi regiment) todithix (rissidtixhi regiment) todtixhi (rissidtixhi regiment) firt (rit regiment) gotto (rit regiment) hinnit (rit regiment) sto (rit regiment) frox (rox regiment) = reduced( x3o3/2x5o , by 2thah ) ipixady (rox regiment) lifpipixhi (rox regiment) nipixady (rox regiment) rixhi (rox regiment) sophi (rox regiment) sprapivady (rox regiment) sriphi (rox regiment) badohi (sabbadipady regiment) bithi (sabbadipady regiment) gabbadipady (sabbadipady regiment) gabbathi (sabbadipady regiment) gabippady (sabbadipady regiment) ganbathi (sabbadipady regiment) ganbippady (sabbadipady regiment) sabbathi (sabbadipady regiment) sabippady (sabbadipady regiment) sanbathi (sabbadipady regiment) sanbippady (sabbadipady regiment) dippit (sidpith regiment) iquipadah (sidpith regiment) shafipto (sidpith regiment) snappoth (sidpith regiment) stefacoth (sidpith regiment) six fipady (sidpixhi regiment) sadtifady (sidtaxhi regiment) = hemi( x5o3/2x5o3/2*a5*c ) sand tathi (sidtaxhi regiment) = reduced( x5x5o3o5/3*a3/2*c , by sitphi ) siddit paxhi (sidtaxhi regiment) sirdatady (sidtaxhi regiment) = reduced( x3/2o3o3o5*a5/3*c , by {5/2} ) sirdtapady (sidtaxhi regiment) = reduced( x5o3x3/2o3*b , by 2tet ) ditdidap (sidtidap regiment) gidtidap (sidtidap regiment) didhi (sishi regiment) gifdahihox (sishi regiment) gridaphi (sishi regiment) gridixhi (sishi regiment) idhi (sishi regiment) ofiddady (sishi regiment) paphacki (sishi regiment) paphicki (sishi regiment) sifdahihox (sishi regiment) sridaphi (sishi regiment) sridixhi (sishi regiment) inpac (spic regiment) piphid (spid regiment) pinpixhi (srahi regiment) spriphi (srahi regiment) = reduced( x5x3o3/2x , by 2thah ) garpop (srip regiment) pinnipdip (srip regiment) pippindip (srip regiment) pirpop (srip regiment) = reduced( x3x3o3/2x , by 2thah ) sirdop (srip regiment) pinpith (srit regiment) spript (srit regiment) = reduced( x4x3o3/2x , by 2thah ) titho (thex regiment) gapript (wavitoth regiment) = reduced( x4/3x3o3/2x , by 2thah ) ... ``` ```gadsadox (???) compound-member: [10raggix] gap (convex, edge skeleton is an ex sub-skeleton) gisp (edge skeleton is a gax sub-skeleton) gondip (edge skeleton is a gittith super-skeleton) ondip (edge skeleton is a sidpith super-skeleton) padiap (edge skeleton is a gax sub-skeleton) rappisdi (edge skeleton is a sishi sub-skeleton) rapsady (???) sabbadipady (edge skeleton is join of quit sishi skeleton with siddapady skeleton) sadsadox (???) compound-member: [10rox] sidtidap (heading the set of Johnson antiprisms) sisp (edge skeleton is an ex sub-skeleton) ... ```