Polytope of Type {12,12}

Play with this polytope as a twisty puzzle

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {12,12}*864m
if this polytope has a name.
Group : SmallGroup(864,4669)
Rank : 3
Schlafli Type : {12,12}
Number of vertices, edges, etc : 36, 216, 36
Order of s₀s₁s₂ : 12
Order of s₀s₁s₂s₁ : 3
Special Properties :
   Compact Hyperbolic Quotient
   Locally Spherical
   Orientable
   Self-Dual
Related Polytopes :
   Facet
   Vertex Figure
   Dual
   Petrial
Facet Of :
   {12,12,2} of size 1728
Vertex Figure Of :
   {2,12,12} of size 1728
Quotients (Maximal Quotients in Boldface) :
   12-fold quotients : {4,4}*72
   36-fold quotients : {3,3}*24
Covers (Minimal Covers in Boldface) :
   2-fold covers : {12,12}*1728z
Irregular Quotients (of which this is a minimal cover):
   None.

Permutation Representation (GAP) :

s0 := ( 2, 3)( 5,13)( 6,15)( 7,14)( 8,16)( 9,25)(10,27)(11,26)(12,28)(18,19)(21,29)(22,31)(23,30)(24,32)(34,35);;
s1 := ( 2, 4)( 5, 9)( 6,12)( 7,11)( 8,10)(14,16)(17,21)(18,24)(19,23)(20,22)(26,28)(29,33)(30,36)(31,35)(32,34);;
s2 := ( 1,20)( 2,18)( 3,19)( 4,17)( 5, 8)( 9,32)(10,30)(11,31)(12,29)(13,16)(21,28)(22,26)(23,27)(24,25)(33,36);;
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, s0*s1*s2*s1*s0*s1*s2*s1*s0*s1*s2*s1, 
s0*s1*s2*s0*s1*s2*s1*s2*s0*s1*s0*s1*s2*s0*s1*s2*s1*s2*s0*s1, 
s0*s1*s0*s1*s0*s2*s1*s0*s1*s2*s1*s2*s1*s2*s1*s0*s2*s1*s2*s1*s0*s1 ];;
poly := F / rels;;

Permutation Representation (Magma) :

s0 := Sym(36)!( 2, 3)( 5,13)( 6,15)( 7,14)( 8,16)( 9,25)(10,27)(11,26)(12,28)(18,19)(21,29)(22,31)(23,30)(24,32)(34,35);
s1 := Sym(36)!( 2, 4)( 5, 9)( 6,12)( 7,11)( 8,10)(14,16)(17,21)(18,24)(19,23)(20,22)(26,28)(29,33)(30,36)(31,35)(32,34);
s2 := Sym(36)!( 1,20)( 2,18)( 3,19)( 4,17)( 5, 8)( 9,32)(10,30)(11,31)(12,29)(13,16)(21,28)(22,26)(23,27)(24,25)(33,36);
poly := sub<Sym(36)|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, s0*s1*s2*s1*s0*s1*s2*s1*s0*s1*s2*s1, 
s0*s1*s2*s0*s1*s2*s1*s2*s0*s1*s0*s1*s2*s0*s1*s2*s1*s2*s0*s1, 
s0*s1*s0*s1*s0*s2*s1*s0*s1*s2*s1*s2*s1*s2*s1*s0*s2*s1*s2*s1*s0*s1 >;

References : None.
to this polytope

Polytope of Type {12,12}

Twisty Puzzle