Polytope of Type {6,12}

Play with this polytope as a twisty puzzle

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {6,12}*432f
if this polytope has a name.
Group : SmallGroup(432,530)
Rank : 3
Schlafli Type : {6,12}
Number of vertices, edges, etc : 18, 108, 36
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 :
   {6,12,2} of size 864
   {6,12,4} of size 1728
Vertex Figure Of :
   {2,6,12} of size 864
   {4,6,12} of size 1728
Quotients (Maximal Quotients in Boldface) :
   2-fold quotients : {6,12}*216b
   3-fold quotients : {6,4}*144
   6-fold quotients : {6,4}*72
   27-fold quotients : {2,4}*16
   54-fold quotients : {2,2}*8
Covers (Minimal Covers in Boldface) :
   2-fold covers : {6,24}*864e, {12,12}*864f
   3-fold covers : {6,12}*1296l, {6,12}*1296n, {6,12}*1296o
   4-fold covers : {6,48}*1728e, {12,12}*1728f, {12,24}*1728g, {24,12}*1728i, {24,12}*1728k, {12,24}*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.
      12 facets:
         12 of {6}*12
      6 vertex figures:
         6 of {12}*24

Permutation Representation (GAP) :

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

Permutation Representation (Magma) :

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

References : None.
to this polytope

Polytope of Type {6,12}

Twisty Puzzle