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

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {2,2,3,5}*240
if this polytope has a name.
Group : SmallGroup(240,190)
Rank : 5
Schlafli Type : {2,2,3,5}
Number of vertices, edges, etc : 2, 2, 6, 15, 10
Order of s₀s₁s₂s₃s₄ : 10
Order of s₀s₁s₂s₃s₄s₃s₂s₁ : 2
Special Properties :
   Degenerate
   Universal
   Non-Orientable
   Flat
Related Polytopes :
   Facet
   Vertex Figure
   Dual
Facet Of :
   {2,2,3,5,2} of size 480
Vertex Figure Of :
   {2,2,2,3,5} of size 480
   {3,2,2,3,5} of size 720
   {4,2,2,3,5} of size 960
   {5,2,2,3,5} of size 1200
   {6,2,2,3,5} of size 1440
   {7,2,2,3,5} of size 1680
   {8,2,2,3,5} of size 1920
Quotients (Maximal Quotients in Boldface) :
   No Regular Quotients.
Covers (Minimal Covers in Boldface) :
   2-fold covers : {4,2,3,5}*480, {2,2,3,5}*480, {2,2,3,10}*480a, {2,2,3,10}*480b, {2,2,6,5}*480b, {2,2,6,5}*480c
   3-fold covers : {6,2,3,5}*720
   4-fold covers : {8,2,3,5}*960, {2,4,6,5}*960b, {4,2,3,5}*960, {4,2,3,10}*960a, {4,2,3,10}*960b, {4,2,6,5}*960b, {4,2,6,5}*960c, {2,2,3,10}*960, {2,2,6,5}*960b, {2,2,6,10}*960c, {2,2,6,10}*960d, {2,2,6,10}*960e, {2,2,6,10}*960f
   5-fold covers : {10,2,3,5}*1200
   6-fold covers : {12,2,3,5}*1440, {2,2,3,10}*1440, {2,2,3,15}*1440, {2,2,6,15}*1440, {2,6,6,5}*1440b, {6,2,3,5}*1440, {6,2,3,10}*1440a, {6,2,3,10}*1440b, {6,2,6,5}*1440b, {6,2,6,5}*1440c
   7-fold covers : {14,2,3,5}*1680
   8-fold covers : {16,2,3,5}*1920, {4,4,6,5}*1920b, {2,8,6,5}*1920b, {8,2,3,5}*1920, {8,2,3,10}*1920a, {8,2,3,10}*1920b, {8,2,6,5}*1920b, {8,2,6,5}*1920c, {2,2,6,20}*1920b, {2,2,6,20}*1920c, {2,2,12,10}*1920c, {2,2,12,10}*1920d, {2,4,6,5}*1920b, {2,4,6,10}*1920d, {2,4,6,10}*1920e, {4,2,3,10}*1920, {4,2,6,5}*1920b, {4,2,6,10}*1920c, {4,2,6,10}*1920d, {4,2,6,10}*1920e, {4,2,6,10}*1920f, {2,2,6,10}*1920b, {2,2,3,20}*1920, {2,2,12,5}*1920
Permutation Representation (GAP) :

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

Permutation Representation (Magma) :

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

to this polytope