Polytope of Type {2,6,20,2}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {2,6,20,2}*960b
if this polytope has a name.
Group : SmallGroup(960,11372)
Rank : 5
Schlafli Type : {2,6,20,2}
Number of vertices, edges, etc : 2, 6, 60, 20, 2
Order of s₀s₁s₂s₃s₄ : 30
Order of s₀s₁s₂s₃s₄s₃s₂s₁ : 2
Special Properties :
   Degenerate
   Universal
   Non-Orientable
   Flat
Related Polytopes :
   Facet
   Vertex Figure
   Dual
Facet Of :
   {2,6,20,2,2} of size 1920
Vertex Figure Of :
   {2,2,6,20,2} of size 1920
Quotients (Maximal Quotients in Boldface) :
   5-fold quotients : {2,6,4,2}*192b
   10-fold quotients : {2,3,4,2}*96
Covers (Minimal Covers in Boldface) :
   2-fold covers : {2,6,20,2}*1920a
Permutation Representation (GAP) :

s0 := (1,2);;
s1 := ( 5, 6)( 9,10)(13,14)(17,18)(21,22);;
s2 := ( 4, 5)( 7,19)( 8,21)( 9,20)(10,22)(11,15)(12,17)(13,16)(14,18);;
s3 := ( 3, 8)( 4, 7)( 5,10)( 6, 9)(11,20)(12,19)(13,22)(14,21)(15,16)(17,18);;
s4 := (23,24);;
poly := Group([s0,s1,s2,s3,s4]);;

Finitely Presented Group Representation (GAP) :

F := FreeGroup("s0","s1","s2","s3","s4");;
s0 := F.1;;  s1 := F.2;;  s2 := F.3;;  s3 := F.4;;  s4 := F.5;;  
rels := [ s0*s0, s1*s1, s2*s2, s3*s3, s4*s4, s0*s1*s0*s1, 
s0*s2*s0*s2, s0*s3*s0*s3, s1*s3*s1*s3, 
s0*s4*s0*s4, s1*s4*s1*s4, s2*s4*s2*s4, 
s3*s4*s3*s4, s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2, 
s1*s2*s1*s2*s3*s2*s3*s2*s1*s3*s2*s3*s2*s3*s2 ];;
poly := F / rels;;

Permutation Representation (Magma) :

s0 := Sym(24)!(1,2);
s1 := Sym(24)!( 5, 6)( 9,10)(13,14)(17,18)(21,22);
s2 := Sym(24)!( 4, 5)( 7,19)( 8,21)( 9,20)(10,22)(11,15)(12,17)(13,16)(14,18);
s3 := Sym(24)!( 3, 8)( 4, 7)( 5,10)( 6, 9)(11,20)(12,19)(13,22)(14,21)(15,16)
(17,18);
s4 := Sym(24)!(23,24);
poly := sub<Sym(24)|s0,s1,s2,s3,s4>;

Finitely Presented Group Representation (Magma) :

poly<s0,s1,s2,s3,s4> := Group< s0,s1,s2,s3,s4 | s0*s0, s1*s1, s2*s2, 
s3*s3, s4*s4, s0*s1*s0*s1, s0*s2*s0*s2, 
s0*s3*s0*s3, s1*s3*s1*s3, s0*s4*s0*s4, 
s1*s4*s1*s4, s2*s4*s2*s4, s3*s4*s3*s4, 
s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2, 
s1*s2*s1*s2*s3*s2*s3*s2*s1*s3*s2*s3*s2*s3*s2 >;

to this polytope