Polytope of Type {5,6,4}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {5,6,4}*960a
Also Known As : {{5,6}₄,{6,4|2}}. if this polytope has another name.
Group : SmallGroup(960,10882)
Rank : 4
Schlafli Type : {5,6,4}
Number of vertices, edges, etc : 20, 60, 48, 4
Order of s₀s₁s₂s₃ : 4
Order of s₀s₁s₂s₃s₂s₁ : 2
Special Properties :
   Universal
   Orientable
   Flat
Related Polytopes :
   Facet
   Vertex Figure
   Dual
Facet Of :
   {5,6,4,2} of size 1920
Vertex Figure Of :
   {2,5,6,4} of size 1920
Quotients (Maximal Quotients in Boldface) :
   2-fold quotients : {5,6,4}*480a, {5,6,2}*480a
   4-fold quotients : {5,6,2}*240a
Covers (Minimal Covers in Boldface) :
   2-fold covers : {5,6,8}*1920a, {10,6,4}*1920c, {5,6,4}*1920, {10,6,4}*1920e
Permutation Representation (GAP) :

s0 := ( 6, 7)( 8, 9)(10,11);;
s1 := ( 5, 6)( 7, 8)(10,11);;
s2 := (3,4)(8,9);;
s3 := (1,3)(2,4);;
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, s1*s2*s3*s2*s1*s2*s3*s2, 
s2*s3*s2*s3*s2*s3*s2*s3, s0*s1*s0*s1*s0*s1*s0*s1*s0*s1, 
s2*s0*s1*s2*s0*s1*s2*s0*s1*s2*s0*s1, 
s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2 ];;
poly := F / rels;;

Permutation Representation (Magma) :

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

References : None.
to this polytope