Polytope of Type {10,24}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {10,24}*960a
if this polytope has a name.
Group : SmallGroup(960,5713)
Rank : 3
Schlafli Type : {10,24}
Number of vertices, edges, etc : 20, 240, 48
Order of s₀s₁s₂ : 8
Order of s₀s₁s₂s₁ : 4
Special Properties :
   Compact Hyperbolic Quotient
   Locally Spherical
   Non-Orientable
Related Polytopes :
   Facet
   Vertex Figure
   Dual
Facet Of :
   {10,24,2} of size 1920
Vertex Figure Of :
   {2,10,24} of size 1920
Quotients (Maximal Quotients in Boldface) :
   2-fold quotients : {10,12}*480a
   4-fold quotients : {10,6}*240a
   8-fold quotients : {5,6}*120a
Covers (Minimal Covers in Boldface) :
   2-fold covers : {10,48}*1920a, {10,48}*1920b, {10,24}*1920c
Permutation Representation (GAP) :

s0 := (10,11)(12,13);;
s1 := ( 1, 2)( 3, 4)( 5, 8)( 6, 7)( 9,10)(11,12);;
s2 := ( 2, 7)( 3, 5)( 6, 8)(12,13);;
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*s2*s1*s0*s1*s2*s1*s0*s1*s2*s1*s0*s1*s2*s1, 
s2*s1*s2*s1*s2*s1*s0*s1*s2*s1*s2*s0*s1*s2*s1*s0*s1, 
s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1, 
s0*s1*s2*s1*s2*s1*s0*s1*s0*s1*s0*s1*s2*s1*s2*s1*s0*s1*s0*s1, 
s2*s0*s1*s2*s1*s2*s0*s1*s2*s0*s1*s2*s0*s1*s2*s1*s2*s0*s1*s2*s0*s1 ];;
poly := F / rels;;

Permutation Representation (Magma) :

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

References : None.
to this polytope