Polytope of Type {4,5}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {4,5}*240
Also Known As : {4,5}₆. if this polytope has another name.
Group : SmallGroup(240,189)
Rank : 3
Schlafli Type : {4,5}
Number of vertices, edges, etc : 24, 60, 30
Order of s₀s₁s₂ : 6
Order of s₀s₁s₂s₁ : 6
Special Properties :
   Compact Hyperbolic Quotient
   Locally Spherical
   Orientable
Related Polytopes :
   Facet
   Vertex Figure
   Dual
   Petrial
   Halving Operation
Facet Of :
   {4,5,2} of size 480
Vertex Figure Of :
   {2,4,5} of size 480
   {4,4,5} of size 960
   {6,4,5} of size 1440
   {8,4,5} of size 1920
Quotients (Maximal Quotients in Boldface) :
   2-fold quotients : {4,5}*120
Covers (Minimal Covers in Boldface) :
   2-fold covers : {8,5}*480, {4,10}*480c
   3-fold covers : {4,15}*720
   4-fold covers : {8,10}*960c, {8,10}*960d, {4,20}*960c, {4,20}*960d, {4,10}*960
   5-fold covers : {4,5}*1200, {20,5}*1200
   6-fold covers : {8,15}*1440, {4,30}*1440, {12,10}*1440g
   7-fold covers : {4,35}*1680
   8-fold covers : {4,20}*1920a, {8,10}*1920a, {4,40}*1920a, {4,40}*1920b, {8,10}*1920b, {4,20}*1920b, {4,10}*1920, {8,20}*1920a, {8,20}*1920b, {8,20}*1920c, {8,20}*1920d, {4,40}*1920c, {4,40}*1920d
Permutation Representation (GAP) :

s0 := (4,5);;
s1 := (2,4)(3,5)(6,7);;
s2 := (1,2)(4,5)(6,7);;
poly := Group([s0,s1,s2]);;

Finitely Presented Group Representation (GAP) :

F := FreeGroup("s0","s1","s2");;
s0 := F.1;;  s1 := F.2;;  s2 := F.3;;  
rels := [ s0*s0, s1*s1, s2*s2, s0*s2*s0*s2, s0*s1*s0*s1*s0*s1*s0*s1, 
s1*s2*s1*s2*s1*s2*s1*s2*s1*s2, s2*s0*s1*s2*s0*s1*s2*s0*s1*s2*s0*s1*s2*s0*s1*s2*s0*s1 ];;
poly := F / rels;;

Permutation Representation (Magma) :

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

Finitely Presented Group Representation (Magma) :

poly<s0,s1,s2> := Group< s0,s1,s2 | s0*s0, s1*s1, s2*s2, 
s0*s2*s0*s2, s0*s1*s0*s1*s0*s1*s0*s1, 
s1*s2*s1*s2*s1*s2*s1*s2*s1*s2, s2*s0*s1*s2*s0*s1*s2*s0*s1*s2*s0*s1*s2*s0*s1*s2*s0*s1 >;

References : None.
to this polytope