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Polytope of Type {10,8}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {10,8}*1440g
if this polytope has a name.
Group : SmallGroup(1440,5843)
Rank : 3
Schlafli Type : {10,8}
Number of vertices, edges, etc : 90, 360, 72
Order of s0s1s2 : 8
Order of s0s1s2s1 : 8
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 : {5,8}*720a
Covers (Minimal Covers in Boldface) :
   None in this atlas.
Permutation Representation (GAP) :
s0 := ( 2, 8)( 3, 6)( 4, 9)( 7,10)(11,12);;
s1 := (1,2)(3,5)(4,6)(7,8);;
s2 := ( 1, 5)( 2, 7)( 3, 9)( 4, 6)( 8,10);;
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, 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*s2*s1*s0*s1*s0*s1*s0*s1*s0*s1*s2*s1*s0*s1*s0*s1*s0*s1, 
s0*s1*s0*s1*s0*s1*s2*s1*s2*s1*s2*s0*s1*s0*s1*s2*s1*s2*s0*s1*s2 ];;
poly := F / rels;;
 
Permutation Representation (Magma) :
s0 := Sym(12)!( 2, 8)( 3, 6)( 4, 9)( 7,10)(11,12);
s1 := Sym(12)!(1,2)(3,5)(4,6)(7,8);
s2 := Sym(12)!( 1, 5)( 2, 7)( 3, 9)( 4, 6)( 8,10);
poly := sub<Sym(12)|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, 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*s2*s1*s0*s1*s0*s1*s0*s1*s0*s1*s2*s1*s0*s1*s0*s1*s0*s1, 
s0*s1*s0*s1*s0*s1*s2*s1*s2*s1*s2*s0*s1*s0*s1*s2*s1*s2*s0*s1*s2 >; 
 
References : None.
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