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Polytope of Type {12,8}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {12,8}*1152c
if this polytope has a name.
Group : SmallGroup(1152,157849)
Rank : 3
Schlafli Type : {12,8}
Number of vertices, edges, etc : 72, 288, 48
Order of s0s1s2 : 4
Order of s0s1s2s1 : 6
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) :
   16-fold quotients : {6,4}*72
Covers (Minimal Covers in Boldface) :
   None in this atlas.
Permutation Representation (GAP) :
s0 := ( 3, 4)( 7, 8)( 9,13)(10,14)(11,16)(12,15);;
s1 := ( 1, 3)( 2, 4)( 5,15)( 6,16)( 7,13)( 8,14)( 9,11)(10,12);;
s2 := ( 2, 5)( 3,13)( 4, 9)( 7,14)( 8,10)(11,16);;
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*s2*s1*s0*s2*s1*s0*s1*s0*s2*s1*s0*s1*s2, 
s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2, 
s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1 ];;
poly := F / rels;;
 
Permutation Representation (Magma) :
s0 := Sym(16)!( 3, 4)( 7, 8)( 9,13)(10,14)(11,16)(12,15);
s1 := Sym(16)!( 1, 3)( 2, 4)( 5,15)( 6,16)( 7,13)( 8,14)( 9,11)(10,12);
s2 := Sym(16)!( 2, 5)( 3,13)( 4, 9)( 7,14)( 8,10)(11,16);
poly := sub<Sym(16)|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*s2*s1*s0*s2*s1*s0*s1*s0*s2*s1*s0*s1*s2, 
s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2, 
s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1 >; 
 
References : None.
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