Polytope of Type {5,3,2,5}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {5,3,2,5}*600
if this polytope has a name.
Group : SmallGroup(600,146)
Rank : 5
Schlafli Type : {5,3,2,5}
Number of vertices, edges, etc : 10, 15, 6, 5, 5
Order of s₀s₁s₂s₃s₄ : 5
Order of s₀s₁s₂s₃s₄s₃s₂s₁ : 2
Special Properties :
   Degenerate
   Universal
   Non-Orientable
   Flat
Related Polytopes :
   Facet
   Vertex Figure
   Dual
Facet Of :
   {5,3,2,5,2} of size 1200
Vertex Figure Of :
   {2,5,3,2,5} of size 1200
Quotients (Maximal Quotients in Boldface) :
   No Regular Quotients.
Covers (Minimal Covers in Boldface) :
   2-fold covers : {5,3,2,5}*1200, {5,3,2,10}*1200, {5,6,2,5}*1200b, {5,6,2,5}*1200c, {10,3,2,5}*1200a, {10,3,2,5}*1200b
   3-fold covers : {5,3,2,15}*1800
Permutation Representation (GAP) :

s0 := (2,3)(4,5);;
s1 := (1,2)(3,4);;
s2 := (2,5)(3,4);;
s3 := ( 7, 8)( 9,10);;
s4 := (6,7)(8,9);;
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*s2*s0*s2, 
s0*s3*s0*s3, s1*s3*s1*s3, s2*s3*s2*s3, 
s0*s4*s0*s4, s1*s4*s1*s4, s2*s4*s2*s4, 
s1*s2*s1*s2*s1*s2, s0*s1*s0*s1*s0*s1*s0*s1*s0*s1, 
s3*s4*s3*s4*s3*s4*s3*s4*s3*s4, s0*s2*s1*s0*s2*s1*s0*s2*s1*s0*s2*s1*s0*s2*s1 ];;
poly := F / rels;;

Permutation Representation (Magma) :

s0 := Sym(10)!(2,3)(4,5);
s1 := Sym(10)!(1,2)(3,4);
s2 := Sym(10)!(2,5)(3,4);
s3 := Sym(10)!( 7, 8)( 9,10);
s4 := Sym(10)!(6,7)(8,9);
poly := sub<Sym(10)|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*s2*s0*s2, s0*s3*s0*s3, 
s1*s3*s1*s3, s2*s3*s2*s3, s0*s4*s0*s4, 
s1*s4*s1*s4, s2*s4*s2*s4, s1*s2*s1*s2*s1*s2, 
s0*s1*s0*s1*s0*s1*s0*s1*s0*s1, s3*s4*s3*s4*s3*s4*s3*s4*s3*s4, 
s0*s2*s1*s0*s2*s1*s0*s2*s1*s0*s2*s1*s0*s2*s1 >;

to this polytope