Polytope of Type {4,5,2}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {4,5,2}*240
if this polytope has a name.
Group : SmallGroup(240,189)
Rank : 4
Schlafli Type : {4,5,2}
Number of vertices, edges, etc : 12, 30, 15, 2
Order of s₀s₁s₂s₃ : 6
Order of s₀s₁s₂s₃s₂s₁ : 2
Special Properties :
   Degenerate
   Universal
   Non-Orientable
   Flat
Related Polytopes :
   Facet
   Vertex Figure
   Dual
Facet Of :
   {4,5,2,2} of size 480
   {4,5,2,3} of size 720
   {4,5,2,4} of size 960
   {4,5,2,5} of size 1200
   {4,5,2,6} of size 1440
   {4,5,2,7} of size 1680
   {4,5,2,8} of size 1920
Vertex Figure Of :
   {2,4,5,2} of size 480
   {4,4,5,2} of size 960
   {6,4,5,2} of size 1440
   {8,4,5,2} of size 1920
Quotients (Maximal Quotients in Boldface) :
   No Regular Quotients.
Covers (Minimal Covers in Boldface) :
   2-fold covers : {4,5,2}*480, {4,10,2}*480a, {4,10,2}*480b
   4-fold covers : {8,5,2}*960, {4,10,4}*960a, {4,10,2}*960a, {4,10,2}*960b, {4,10,2}*960c
   6-fold covers : {4,10,6}*1440, {4,15,2}*1440, {12,10,2}*1440
   8-fold covers : {8,10,2}*1920a, {8,10,2}*1920b, {4,10,8}*1920, {4,10,2}*1920, {4,10,4}*1920b, {4,20,2}*1920a, {4,20,2}*1920b, {4,20,2}*1920c, {4,20,2}*1920d, {8,10,2}*1920c, {8,10,2}*1920d
Permutation Representation (GAP) :

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

Permutation Representation (Magma) :

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

to this polytope