Polytope of Type {10,40}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {10,40}*960a
if this polytope has a name.
Group : SmallGroup(960,5739)
Rank : 3
Schlafli Type : {10,40}
Number of vertices, edges, etc : 12, 240, 48
Order of s₀s₁s₂ : 24
Order of s₀s₁s₂s₁ : 6
Special Properties :
   Compact Hyperbolic Quotient
   Locally Spherical
   Non-Orientable
Related Polytopes :
   Facet
   Vertex Figure
   Dual
Facet Of :
   {10,40,2} of size 1920
Vertex Figure Of :
   {2,10,40} of size 1920
Quotients (Maximal Quotients in Boldface) :
   2-fold quotients : {10,20}*480a
   4-fold quotients : {10,10}*240a
   8-fold quotients : {5,10}*120b, {10,5}*120b
   16-fold quotients : {5,5}*60
Covers (Minimal Covers in Boldface) :
   2-fold covers : {10,80}*1920a, {10,80}*1920b, {10,40}*1920a
Permutation Representation (GAP) :

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

Permutation Representation (Magma) :

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

References : None.
to this polytope