Polytope of Type {12,6}

Play with this polytope as a twisty puzzle

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {12,6}*432f
if this polytope has a name.
Group : SmallGroup(432,530)
Rank : 3
Schlafli Type : {12,6}
Number of vertices, edges, etc : 36, 108, 18
Order of s₀s₁s₂ : 4
Order of s₀s₁s₂s₁ : 6
Special Properties :
   Compact Hyperbolic Quotient
   Locally Spherical
   Orientable
Related Polytopes :
   Facet
   Vertex Figure
   Dual
   Petrial
Facet Of :
   {12,6,2} of size 864
   {12,6,4} of size 1728
Vertex Figure Of :
   {2,12,6} of size 864
   {4,12,6} of size 1728
Quotients (Maximal Quotients in Boldface) :
   2-fold quotients : {12,6}*216a
   3-fold quotients : {4,6}*144
   6-fold quotients : {4,6}*72
   27-fold quotients : {4,2}*16
   54-fold quotients : {2,2}*8
Covers (Minimal Covers in Boldface) :
   2-fold covers : {24,6}*864e, {12,12}*864e
   3-fold covers : {12,6}*1296j, {12,6}*1296m, {12,6}*1296o
   4-fold covers : {48,6}*1728d, {12,12}*1728d, {24,12}*1728g, {12,24}*1728i, {12,24}*1728k, {24,12}*1728m
Irregular Quotients (of which this is a minimal cover):
   P/N, where N=<s1*s0*s1*s2*s1*s0*s1*s2> of order 3.
      6 facets:
         6 of {12}*24
      12 vertex figures:
         12 of {6}*12

Permutation Representation (GAP) :

s0 := ( 2, 3)( 5, 6)( 8, 9)(10,19)(11,21)(12,20)(13,22)(14,24)(15,23)(16,25)(17,27)(18,26)(29,30)(32,33)(35,36)(37,46)(38,48)(39,47)(40,49)(41,51)(42,50)(43,52)(44,54)(45,53);;
s1 := ( 1, 2)( 4,20)( 5,19)( 6,21)( 7,11)( 8,10)( 9,12)(13,27)(14,26)(15,25)(17,18)(23,24)(28,29)(31,47)(32,46)(33,48)(34,38)(35,37)(36,39)(40,54)(41,53)(42,52)(44,45)(50,51);;
s2 := ( 1,31)( 2,32)( 3,33)( 4,28)( 5,29)( 6,30)( 7,34)( 8,35)( 9,36)(10,49)(11,50)(12,51)(13,46)(14,47)(15,48)(16,52)(17,53)(18,54)(19,40)(20,41)(21,42)(22,37)(23,38)(24,39)(25,43)(26,44)(27,45);;
poly := Group([s0,s1,s2]);;

Finitely Presented Group Representation (GAP) :

F := FreeGroup("s0","s1","s2");;
s0 := F.1;;  s1 := F.2;;  s2 := F.3;;  
rels := [ s0*s0, s1*s1, s2*s2, s0*s2*s0*s2, s2*s0*s1*s2*s0*s1*s2*s0*s1*s2*s0*s1, 
s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2, 
s0*s1*s0*s1*s0*s1*s2*s1*s0*s1*s0*s1*s0*s1*s2*s1 ];;
poly := F / rels;;

Permutation Representation (Magma) :

s0 := Sym(54)!( 2, 3)( 5, 6)( 8, 9)(10,19)(11,21)(12,20)(13,22)(14,24)(15,23)(16,25)(17,27)(18,26)(29,30)(32,33)(35,36)(37,46)(38,48)(39,47)(40,49)(41,51)(42,50)(43,52)(44,54)(45,53);
s1 := Sym(54)!( 1, 2)( 4,20)( 5,19)( 6,21)( 7,11)( 8,10)( 9,12)(13,27)(14,26)(15,25)(17,18)(23,24)(28,29)(31,47)(32,46)(33,48)(34,38)(35,37)(36,39)(40,54)(41,53)(42,52)(44,45)(50,51);
s2 := Sym(54)!( 1,31)( 2,32)( 3,33)( 4,28)( 5,29)( 6,30)( 7,34)( 8,35)( 9,36)(10,49)(11,50)(12,51)(13,46)(14,47)(15,48)(16,52)(17,53)(18,54)(19,40)(20,41)(21,42)(22,37)(23,38)(24,39)(25,43)(26,44)(27,45);
poly := sub<Sym(54)|s0,s1,s2>;

Finitely Presented Group Representation (Magma) :

poly<s0,s1,s2> := Group< s0,s1,s2 | s0*s0, s1*s1, s2*s2, 
s0*s2*s0*s2, s2*s0*s1*s2*s0*s1*s2*s0*s1*s2*s0*s1, 
s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2, 
s0*s1*s0*s1*s0*s1*s2*s1*s0*s1*s0*s1*s0*s1*s2*s1 >;

References : None.
to this polytope

Polytope of Type {12,6}

Twisty Puzzle