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Polytope of Type {6,4}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {6,4}*672c
if this polytope has a name.
Group : SmallGroup(672,1254)
Rank : 3
Schlafli Type : {6,4}
Number of vertices, edges, etc : 84, 168, 56
Order of s0s1s2 : 8
Order of s0s1s2s1 : 8
Special Properties :
   Compact Hyperbolic Quotient
   Locally Spherical
   Orientable
Related Polytopes :
   Facet
   Vertex Figure
   Dual
   Petrial
   Skewing Operation
Facet Of :
   {6,4,2} of size 1344
Vertex Figure Of :
   {2,6,4} of size 1344
Quotients (Maximal Quotients in Boldface) :
   2-fold quotients : {6,4}*336
Covers (Minimal Covers in Boldface) :
   2-fold covers : {6,8}*1344a, {6,8}*1344b, {6,4}*1344
Permutation Representation (GAP) :
s0 := (3,7)(4,8)(5,6);;
s1 := ( 1, 3)( 2, 5)( 4, 8)( 6, 7)( 9,10);;
s2 := ( 1, 2)( 3, 4)( 5, 6)( 7, 8)( 9,10);;
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, 
s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1, 
s0*s1*s2*s1*s0*s1*s0*s1*s2*s1*s0*s1*s0*s1*s2*s1*s0*s1 ];;
poly := F / rels;;
 
Permutation Representation (Magma) :
s0 := Sym(10)!(3,7)(4,8)(5,6);
s1 := Sym(10)!( 1, 3)( 2, 5)( 4, 8)( 6, 7)( 9,10);
s2 := Sym(10)!( 1, 2)( 3, 4)( 5, 6)( 7, 8)( 9,10);
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, s1*s2*s1*s2*s1*s2*s1*s2, 
s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1, 
s0*s1*s2*s1*s0*s1*s0*s1*s2*s1*s0*s1*s0*s1*s2*s1*s0*s1 >; 
 
References : None.
to this polytope