Polytope of Type {5,6,4}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {5,6,4}*480a
if this polytope has a name.
Group : SmallGroup(480,951)
Rank : 4
Schlafli Type : {5,6,4}
Number of vertices, edges, etc : 10, 30, 24, 4
Order of s₀s₁s₂s₃ : 4
Order of s₀s₁s₂s₃s₂s₁ : 2
Special Properties :
   Universal
   Non-Orientable
   Flat
Related Polytopes :
   Facet
   Vertex Figure
   Dual
Facet Of :
   {5,6,4,2} of size 960
   {5,6,4,4} of size 1920
Vertex Figure Of :
   {2,5,6,4} of size 960
Quotients (Maximal Quotients in Boldface) :
   2-fold quotients : {5,6,2}*240a
Covers (Minimal Covers in Boldface) :
   2-fold covers : {5,6,8}*960a, {5,6,4}*960a, {10,6,4}*960a, {10,6,4}*960b
   3-fold covers : {5,6,12}*1440a
   4-fold covers : {5,6,16}*1920a, {10,12,4}*1920d, {10,12,4}*1920e, {5,6,8}*1920a, {10,6,8}*1920c, {10,6,8}*1920d, {10,6,4}*1920c, {5,6,4}*1920, {10,6,4}*1920e
Permutation Representation (GAP) :

s0 := (6,7)(8,9);;
s1 := (5,6)(7,8);;
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, 
s0*s1*s2*s1*s0*s2*s1*s0*s1*s0*s2*s1*s0*s1*s2 ];;
poly := F / rels;;

Permutation Representation (Magma) :

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

References : None.
to this polytope