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

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

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

Permutation Representation (Magma) :

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

to this polytope