Polytope of Type {8,4,5}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {8,4,5}*960
if this polytope has a name.
Group : SmallGroup(960,5713)
Rank : 4
Schlafli Type : {8,4,5}
Number of vertices, edges, etc : 8, 48, 30, 15
Order of s₀s₁s₂s₃ : 24
Order of s₀s₁s₂s₃s₂s₁ : 2
Special Properties :
   Universal
   Non-Orientable
   Flat
Related Polytopes :
   Facet
   Vertex Figure
   Dual
Facet Of :
   {8,4,5,2} of size 1920
Vertex Figure Of :
   {2,8,4,5} of size 1920
Quotients (Maximal Quotients in Boldface) :
   2-fold quotients : {4,4,5}*480
   4-fold quotients : {2,4,5}*240
Covers (Minimal Covers in Boldface) :
   2-fold covers : {16,4,5}*1920, {8,4,5}*1920, {8,4,10}*1920a, {8,4,10}*1920b
Permutation Representation (GAP) :

s0 := (1,2)(3,4)(5,8)(6,7);;
s1 := ( 2, 7)( 3, 5)( 6, 8)(12,13);;
s2 := (10,12)(11,13);;
s3 := ( 9,10)(12,13);;
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*s2*s0*s2, 
s0*s3*s0*s3, s1*s3*s1*s3, s0*s1*s2*s1*s0*s1*s2*s1, 
s1*s2*s1*s2*s1*s2*s1*s2, s2*s3*s2*s3*s2*s3*s2*s3*s2*s3, 
s2*s3*s2*s1*s2*s3*s1*s2*s1*s2*s3*s2*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(13)!(1,2)(3,4)(5,8)(6,7);
s1 := Sym(13)!( 2, 7)( 3, 5)( 6, 8)(12,13);
s2 := Sym(13)!(10,12)(11,13);
s3 := Sym(13)!( 9,10)(12,13);
poly := sub<Sym(13)|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*s2*s0*s2, s0*s3*s0*s3, s1*s3*s1*s3, 
s0*s1*s2*s1*s0*s1*s2*s1, s1*s2*s1*s2*s1*s2*s1*s2, 
s2*s3*s2*s3*s2*s3*s2*s3*s2*s3, s2*s3*s2*s1*s2*s3*s1*s2*s1*s2*s3*s2*s1, 
s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1 >;

References : None.
to this polytope