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

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {5,5,2,3}*360
if this polytope has a name.
Group : SmallGroup(360,121)
Rank : 5
Schlafli Type : {5,5,2,3}
Number of vertices, edges, etc : 6, 15, 6, 3, 3
Order of s₀s₁s₂s₃s₄ : 3
Order of s₀s₁s₂s₃s₄s₃s₂s₁ : 2
Special Properties :
   Degenerate
   Universal
   Non-Orientable
   Flat
Related Polytopes :
   Facet
   Vertex Figure
   Dual
Facet Of :
   {5,5,2,3,2} of size 720
   {5,5,2,3,3} of size 1440
   {5,5,2,3,4} of size 1440
Vertex Figure Of :
   {2,5,5,2,3} of size 720
Quotients (Maximal Quotients in Boldface) :
   No Regular Quotients.
Covers (Minimal Covers in Boldface) :
   2-fold covers : {5,5,2,3}*720, {5,5,2,6}*720, {5,10,2,3}*720a, {5,10,2,3}*720b, {10,5,2,3}*720a, {10,5,2,3}*720b
   3-fold covers : {5,5,2,9}*1080
   4-fold covers : {5,5,2,12}*1440, {5,5,2,6}*1440, {5,10,2,3}*1440, {5,10,2,6}*1440a, {5,10,2,6}*1440b, {10,5,2,3}*1440, {10,5,2,6}*1440a, {10,5,2,6}*1440b, {10,10,2,3}*1440a, {10,10,2,3}*1440b, {10,10,2,3}*1440c, {10,10,2,3}*1440d
   5-fold covers : {5,5,2,15}*1800
Permutation Representation (GAP) :

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

Permutation Representation (Magma) :

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

to this polytope