Polytope of Type {2,4,5}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {2,4,5}*240
if this polytope has a name.
Group : SmallGroup(240,189)
Rank : 4
Schlafli Type : {2,4,5}
Number of vertices, edges, etc : 2, 12, 30, 15
Order of s₀s₁s₂s₃ : 6
Order of s₀s₁s₂s₃s₂s₁ : 2
Special Properties :
   Degenerate
   Universal
   Non-Orientable
   Flat
Related Polytopes :
   Facet
   Vertex Figure
   Dual
Facet Of :
   {2,4,5,2} of size 480
Vertex Figure Of :
   {2,2,4,5} of size 480
   {3,2,4,5} of size 720
   {4,2,4,5} of size 960
   {5,2,4,5} of size 1200
   {6,2,4,5} of size 1440
   {7,2,4,5} of size 1680
   {8,2,4,5} of size 1920
Quotients (Maximal Quotients in Boldface) :
   No Regular Quotients.
Covers (Minimal Covers in Boldface) :
   2-fold covers : {4,4,5}*480, {2,4,5}*480, {2,4,10}*480a, {2,4,10}*480b
   3-fold covers : {6,4,5}*720
   4-fold covers : {8,4,5}*960, {2,8,5}*960, {4,4,5}*960, {4,4,10}*960a, {4,4,10}*960b, {2,4,10}*960a, {2,4,10}*960b, {2,4,10}*960c
   5-fold covers : {10,4,5}*1200
   6-fold covers : {12,4,5}*1440, {6,4,5}*1440, {2,4,15}*1440, {6,4,10}*1440a, {6,4,10}*1440b, {2,12,10}*1440
   7-fold covers : {14,4,5}*1680
   8-fold covers : {16,4,5}*1920, {4,4,10}*1920a, {4,4,10}*1920b, {8,4,5}*1920, {8,4,10}*1920a, {8,4,10}*1920b, {2,8,10}*1920a, {2,8,10}*1920b, {4,4,10}*1920c, {2,4,10}*1920, {2,4,20}*1920a, {2,4,20}*1920b, {4,8,5}*1920, {2,4,20}*1920c, {2,4,20}*1920d, {2,8,10}*1920c, {2,8,10}*1920d
Permutation Representation (GAP) :

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

Permutation Representation (Magma) :

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

to this polytope