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---- 4D ----

This page is available sorted by point-group symmetry (below)
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
other
Wythoffians
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 and
holosnubs
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
other
Wythoffians
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 and
holosnubs
...
...
...


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
other
Wythoffians
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 and
holosnubs
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
other
Wythoffians
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 and
holosnubs
...
...
...
...


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
other
Wythoffians
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 and
holosnubs
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 *)
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
other
Wythoffians
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 and
holosnubs
...
...
...


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
other
Wythoffians
x3x3o5o - tex
x3o3x5o - srix
x3o3o5x - sidpixhi
o3x3x5o - xhi
o3x3o5x - srahi
o3o3x5x - thi
x3x3x5o - grix
x3x3o5x - prahi
x3o3x5x - prix
o3x3x5x - grahi
x3x3x5x - gidpixhi
x3/2x3o5o - [Grünbaumian]
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 - [Grünbaumian]
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 and
holosnubs
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
other
Wythoffians
x3/2x3/2o5o - [Grünbaumian]
x3/2o3/2x5o - srix
x3/2o3/2o5x - sidpixhi
o3/2x3/2x5o - [Grünbaumian]
o3/2x3/2o5x - (contains gicdatrid)
o3/2o3/2x5x - thi
x3/2x3/2x5o - [Grünbaumian]
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 - [Grünbaumian]
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 - [Grünbaumian]
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 - [Grünbaumian]
x3/2o3/2x5/4o - srix
x3/2o3/2o5/4x - saquid paxhi
o3/2x3/2x5/4o - [Grünbaumian]
o3/2x3/2o5/4x - srahi
o3/2o3/2x5/4x - [Grünbaumian]
x3/2x3/2x5/4o - [Grünbaumian]
x3/2x3/2o5/4x - [Grünbaumian]
x3/2o3/2x5/4x - [Grünbaumian]
o3/2x3/2x5/4x - [Grünbaumian]
x3/2x3/2x5/4x - [Grünbaumian]
(partial)
snubs and
holosnubs
...
...
...
...


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
other
Wythoffians
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 and
holosnubs
...
...
...
...
  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
other
Wythoffians
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 and
holosnubs
...
...
...
...


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
other
Wythoffians
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 and
holosnubs
...
...
...
...
  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
other
Wythoffians
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 and
holosnubs
...
...
...
...


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
other
Wythoffians
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 and
holosnubs
...
...
...
...
  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
other
Wythoffians
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 and
holosnubs
...
...
...
...


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
other
Wythoffians
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 and
holosnubs
...
...
...
...
  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
other
Wythoffians
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 and
holosnubs
...
...
...
...


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
other
Wythoffians
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 and
holosnubs
...
...
...
  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
other
Wythoffians
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 and
holosnubs
...
...
...


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
other
Wythoffians
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 and
holosnubs
...
...
...
  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
other
Wythoffians
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 and
holosnubs
...
...
...


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
other
Wythoffians
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 and
holosnubs
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
...
...
...


(Multi-) Prism Symmetries   (up)


Tetrahedral Prism Symmetries   (up)

  o o3o3o (convex) o o3/2o3o3*b (µ=2) o o3/2o3o (µ=3)
quasiregular
components
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
other
Wythoffians
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 - (contains "2thah")
x o3/2x3x - tuttip
x x3/2x3x - (contains "cho+4{6/2}")
(partial)
snubs and
holosnubs
x2s3s3s - ipe
x s3s3s - ipe
...
...
...
  o o3/2o3/2o (µ=5) o o3/2o3/2o3/2*b (µ=6)  
quasiregular
components
x x3/2o3/2o - tepe
x o3/2x3/2o - ope
x x3/2o3/2o3/2*b - (contains "2tet")
 
other
Wythoffians
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 and
holosnubs
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)
quasiregular
components
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
other
Wythoffians
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 and
holosnubs
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)  
quasiregular
components
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")
 
other
Wythoffians
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 and
holosnubs
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)
quasiregular
components
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")
other
Wythoffians
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 and
holosnubs
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)
quasiregular
components
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")
other
Wythoffians
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 and
holosnubs
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)
quasiregular
components
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
other
Wythoffians
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 and
holosnubs
...
...
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)
quasiregular
components
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)
other
Wythoffians
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 and
holosnubs
...
x s5/3s5s - isdiddip
...
...
  o o5/3o5/2o3*b (µ=10) o o3/2o5o (µ=11) o o5/3o3o (µ=13)
quasiregular
components
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
other
Wythoffians
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 and
holosnubs
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)
quasiregular
components
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)
other
Wythoffians
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 and
holosnubs
...
...
...
  o o3/2o5/2o (µ=17) o o3/2o5/3o3*b (µ=18) o o5/3o5/3o5/2*b (µ=18)
quasiregular
components
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")
other
Wythoffians
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 and
holosnubs
...
...
...
  o o5/4o3o (µ=19) o o5/4o5/2o (µ=21) o o3/2o3/2o5/2*b (µ=22)
quasiregular
components
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")
other
Wythoffians
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 and
holosnubs
...
...
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)
quasiregular
components
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
other
Wythoffians
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 and
holosnubs
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)
quasiregular
components
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")
other
Wythoffians
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 and
holosnubs
...
...
...
  o o5/4o5/4o3/2*b (µ=38) o o5/4o5/4o5/4*b (µ=42)  
quasiregular
components
x x5/4o5/4o3/2*b - (contains cid)
x o5/4x5/4o3/2*b - (contains "2doe")
x x5/4o5/4o5/4*b - (contains "2gad")
 
other
Wythoffians
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 and
holosnubs
...
...
 


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
other
Wythoffians
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 and
holosnubs
s4o2s4o   - hex

s3s2x3o   - triddip
s3s x3o   - triddip
s3s2x3x   - thiddip
s3s x3x   - thiddip

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
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)

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)

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)


...


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