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Polytope of Type {2,5,8}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {2,5,8}*1440a
if this polytope has a name.
Group : SmallGroup(1440,5843)
Rank : 4
Schlafli Type : {2,5,8}
Number of vertices, edges, etc : 2, 45, 180, 72
Order of s0s1s2s3 : 8
Order of s0s1s2s3s2s1 : 2
Special Properties :
   Degenerate
   Universal
   Non-Orientable
   Flat
Related Polytopes :
   Facet
   Vertex Figure
   Dual
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 := (1,2);;
s1 := ( 4,10)( 5, 7)( 6, 9)( 8,11);;
s2 := ( 3, 4)( 6,12)( 7,10)( 8, 9);;
s3 := ( 3,12)( 4, 5)( 6, 8)( 7,10)( 9,11);;
poly := Group([s0,s1,s2,s3]);;
 
Finitely Presented Group Representation (GAP) :
F := FreeGroup("s0","s1","s2","s3");;
s0 := F.1;;  s1 := F.2;;  s2 := F.3;;  s3 := F.4;;  
rels := [ s0*s0, s1*s1, s2*s2, s3*s3, s0*s1*s0*s1, 
s0*s2*s0*s2, s0*s3*s0*s3, s1*s3*s1*s3, 
s1*s2*s1*s2*s1*s2*s1*s2*s1*s2, s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3, 
s1*s2*s3*s2*s3*s2*s1*s2*s3*s2*s3*s2*s1*s2*s3*s2*s3*s2, 
s1*s2*s1*s2*s3*s2*s3*s1*s2*s3*s2*s1*s2*s3*s1*s2*s3*s2*s3 ];;
poly := F / rels;;
 
Permutation Representation (Magma) :
s0 := Sym(12)!(1,2);
s1 := Sym(12)!( 4,10)( 5, 7)( 6, 9)( 8,11);
s2 := Sym(12)!( 3, 4)( 6,12)( 7,10)( 8, 9);
s3 := Sym(12)!( 3,12)( 4, 5)( 6, 8)( 7,10)( 9,11);
poly := sub<Sym(12)|s0,s1,s2,s3>;
 
Finitely Presented Group Representation (Magma) :
poly<s0,s1,s2,s3> := Group< s0,s1,s2,s3 | s0*s0, s1*s1, s2*s2, 
s3*s3, s0*s1*s0*s1, s0*s2*s0*s2, s0*s3*s0*s3, 
s1*s3*s1*s3, s1*s2*s1*s2*s1*s2*s1*s2*s1*s2, 
s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3, 
s1*s2*s3*s2*s3*s2*s1*s2*s3*s2*s3*s2*s1*s2*s3*s2*s3*s2, 
s1*s2*s1*s2*s3*s2*s3*s1*s2*s3*s2*s1*s2*s3*s1*s2*s3*s2*s3 >; 
 

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