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# Polytope of Type {8,8}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {8,8}*1440b
if this polytope has a name.
Group : SmallGroup(1440,5841)
Rank : 3
Schlafli Type : {8,8}
Number of vertices, edges, etc : 90, 360, 90
Order of s0s1s2 : 8
Order of s0s1s2s1 : 4
Special Properties :
Compact Hyperbolic Quotient
Locally Spherical
Orientable
Self-Dual
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) :
No Regular Quotients.
Covers (Minimal Covers in Boldface) :
None in this atlas.
Permutation Representation (GAP) :
s0 := ( 2, 9)( 4, 6)( 7,10);;
s1 := ( 1, 2)( 3, 5)( 4, 9)( 6, 7)( 8,10);;
s2 := ( 3, 8)( 4, 7)( 6,10);;
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, s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1,
s0*s1*s2*s1*s0*s1*s2*s1*s0*s1*s2*s1*s0*s1*s2*s1,
s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2,
s2*s0*s1*s2*s0*s1*s2*s0*s1*s2*s1*s2*s0*s1*s2*s0*s1*s2*s0*s1*s0*s1,
s0*s2*s1*s2*s1*s0*s2*s1*s0*s1*s0*s1*s2*s0*s1*s2*s1*s2*s0*s1*s2*s1*s2*s1 ];;
poly := F / rels;;

Permutation Representation (Magma) :
s0 := Sym(10)!( 2, 9)( 4, 6)( 7,10);
s1 := Sym(10)!( 1, 2)( 3, 5)( 4, 9)( 6, 7)( 8,10);
s2 := Sym(10)!( 3, 8)( 4, 7)( 6,10);
poly := sub<Sym(10)|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*s0*s1*s0*s1*s0*s1,
s0*s1*s2*s1*s0*s1*s2*s1*s0*s1*s2*s1*s0*s1*s2*s1,
s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2,
s2*s0*s1*s2*s0*s1*s2*s0*s1*s2*s1*s2*s0*s1*s2*s0*s1*s2*s0*s1*s0*s1,
s0*s2*s1*s2*s1*s0*s2*s1*s0*s1*s0*s1*s2*s0*s1*s2*s1*s2*s0*s1*s2*s1*s2*s1 >;

References : None.
to this polytope