Polytope of Type {4,3,2,5}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {4,3,2,5}*240
if this polytope has a name.
Group : SmallGroup(240,194)
Rank : 5
Schlafli Type : {4,3,2,5}
Number of vertices, edges, etc : 4, 6, 3, 5, 5
Order of s₀s₁s₂s₃s₄ : 15
Order of s₀s₁s₂s₃s₄s₃s₂s₁ : 2
Special Properties :
   Degenerate
   Universal
   Non-Orientable
   Flat
Related Polytopes :
   Facet
   Vertex Figure
   Dual
Facet Of :
   {4,3,2,5,2} of size 480
   {4,3,2,5,3} of size 1440
   {4,3,2,5,5} of size 1440
Vertex Figure Of :
   {2,4,3,2,5} of size 480
   {4,4,3,2,5} of size 1920
Quotients (Maximal Quotients in Boldface) :
   No Regular Quotients.
Covers (Minimal Covers in Boldface) :
   2-fold covers : {4,3,2,5}*480, {4,3,2,10}*480, {4,6,2,5}*480b, {4,6,2,5}*480c
   3-fold covers : {4,9,2,5}*720, {4,3,2,15}*720
   4-fold covers : {4,12,2,5}*960b, {4,12,2,5}*960c, {4,3,2,20}*960, {8,3,2,5}*960, {4,3,2,10}*960, {4,6,2,5}*960, {4,6,2,10}*960b, {4,6,2,10}*960c
   5-fold covers : {4,3,2,25}*1200, {4,15,2,5}*1200
   6-fold covers : {4,9,2,5}*1440, {4,9,2,10}*1440, {4,18,2,5}*1440b, {4,18,2,5}*1440c, {4,3,6,10}*1440, {12,3,2,5}*1440, {12,6,2,5}*1440d, {4,3,2,15}*1440, {4,3,2,30}*1440, {4,6,2,15}*1440b, {4,6,2,15}*1440c
   7-fold covers : {4,21,2,5}*1680, {4,3,2,35}*1680
   8-fold covers : {4,6,2,5}*1920a, {8,3,2,5}*1920, {8,6,2,5}*1920a, {4,24,2,5}*1920c, {4,24,2,5}*1920d, {4,3,2,40}*1920, {4,12,2,5}*1920b, {4,12,2,10}*1920b, {4,12,2,10}*1920c, {4,3,2,20}*1920, {4,6,2,20}*1920b, {4,6,2,20}*1920c, {4,6,4,10}*1920b, {4,6,2,5}*1920b, {4,12,2,5}*1920c, {8,3,2,10}*1920, {8,6,2,5}*1920b, {8,6,2,5}*1920c, {4,6,2,10}*1920, {4,3,4,10}*1920
Permutation Representation (GAP) :

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

Permutation Representation (Magma) :

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

to this polytope