Polytope of Type {5,5}

Play with this polytope as a twisty puzzle

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {5,5}*1920c
if this polytope has a name.
Group : SmallGroup(1920,241004)
Rank : 3
Schlafli Type : {5,5}
Number of vertices, edges, etc : 192, 480, 192
Order of s0s1s2 : 12
Order of s0s1s2s1 : 12
Special Properties :
   Compact Hyperbolic Quotient
   Locally Spherical
   Non-Orientable
Related Polytopes :
   Facet
   Vertex Figure
   Dual
   Petrial
Facet Of :
   None in this Atlas
Vertex Figure Of :
   None in this Atlas
Quotients (Maximal Quotients in Boldface) :
   2-fold quotients : {5,5}*960
   32-fold quotients : {5,5}*60
Covers (Minimal Covers in Boldface) :
   None in this atlas.
Irregular Quotients (of which this is a minimal cover):
   P/N, where N=<s1*s0*s2*s1*s0*s1*s2*s1*s2*s1*s0*s1*s0*s2*s1*s2> of order 2.
      96 facets:
         96 of {5}*10
      96 vertex figures:
         96 of {5}*10
   P/N, where N=<s1*s0*s1*s2*s1*s0*s2*s1*s0*s1*s2*s1*s2> of order 3.
      64 facets:
         64 of {5}*10
      64 vertex figures:
         64 of {5}*10

Permutation Representation (GAP) : 
s0 := ( 3, 4)( 5,15)( 7, 8)( 9,30)(11,16)(12,17)(13,25)(14,19)(18,29)(20,31)(21,28)(22,27)(23,32)(24,26);;
s1 := ( 1, 3)( 2,27)( 4,21)( 5,17)( 6,14)( 7,15)( 8,16)(10,29)(11,32)(12,23)(13,19)(18,31)(22,30)(24,26);;
s2 := ( 1, 6)( 2,10)( 3,23)( 4,32)( 5,14)( 7,20)( 8,31)( 9,11)(12,24)(15,19)(16,30)(17,26)(18,29)(22,27);;
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*s0*s1*s0*s1*s0*s1*s0*s1, 
s1*s2*s1*s2*s1*s2*s1*s2*s1*s2, s1*s0*s1*s0*s1*s2*s1*s0*s1*s0*s2*s1*s0*s1*s0*s2*s1*s0*s1*s0*s2*s1*s0*s1*s2, 
s0*s1*s0*s1*s2*s1*s2*s0*s1*s2*s1*s0*s1*s2*s0*s1*s2*s1*s0*s1*s2*s1*s0*s1*s2*s1*s2 ];;
poly := F / rels;;
Permutation Representation (Magma) : 
s0 := Sym(32)!( 3, 4)( 5,15)( 7, 8)( 9,30)(11,16)(12,17)(13,25)(14,19)(18,29)(20,31)(21,28)(22,27)(23,32)(24,26);
s1 := Sym(32)!( 1, 3)( 2,27)( 4,21)( 5,17)( 6,14)( 7,15)( 8,16)(10,29)(11,32)(12,23)(13,19)(18,31)(22,30)(24,26);
s2 := Sym(32)!( 1, 6)( 2,10)( 3,23)( 4,32)( 5,14)( 7,20)( 8,31)( 9,11)(12,24)(15,19)(16,30)(17,26)(18,29)(22,27);
poly := sub<Sym(32)|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*s0*s1*s0*s1*s0*s1*s0*s1, 
s1*s2*s1*s2*s1*s2*s1*s2*s1*s2, s1*s0*s1*s0*s1*s2*s1*s0*s1*s0*s2*s1*s0*s1*s0*s2*s1*s0*s1*s0*s2*s1*s0*s1*s2, 
s0*s1*s0*s1*s2*s1*s2*s0*s1*s2*s1*s0*s1*s2*s0*s1*s2*s1*s0*s1*s2*s1*s0*s1*s2*s1*s2 >;
References : None.
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