Polytope of Type {5,2,24}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {5,2,24}*480
if this polytope has a name.
Group : SmallGroup(480,324)
Rank : 4
Schlafli Type : {5,2,24}
Number of vertices, edges, etc : 5, 5, 24, 24
Order of s₀s₁s₂s₃ : 120
Order of s₀s₁s₂s₃s₂s₁ : 2
Special Properties :
   Degenerate
   Universal
   Orientable
   Flat
Related Polytopes :
   Facet
   Vertex Figure
   Dual
Facet Of :
   {5,2,24,2} of size 960
   {5,2,24,4} of size 1920
   {5,2,24,4} of size 1920
   {5,2,24,4} of size 1920
   {5,2,24,4} of size 1920
Vertex Figure Of :
   {2,5,2,24} of size 960
Quotients (Maximal Quotients in Boldface) :
   2-fold quotients : {5,2,12}*240
   3-fold quotients : {5,2,8}*160
   4-fold quotients : {5,2,6}*120
   6-fold quotients : {5,2,4}*80
   8-fold quotients : {5,2,3}*60
   12-fold quotients : {5,2,2}*40
Covers (Minimal Covers in Boldface) :
   2-fold covers : {5,2,48}*960, {10,2,24}*960
   3-fold covers : {5,2,72}*1440, {15,2,24}*1440
   4-fold covers : {5,2,96}*1920, {10,4,24}*1920a, {20,2,24}*1920, {10,2,48}*1920
Permutation Representation (GAP) :

s0 := (2,3)(4,5);;
s1 := (1,2)(3,4);;
s2 := ( 7, 8)( 9,10)(11,14)(12,16)(13,15)(17,20)(18,22)(19,21)(24,27)(25,26)
(28,29);;
s3 := ( 6,12)( 7, 9)( 8,18)(10,13)(11,15)(14,24)(16,19)(17,21)(20,28)(22,25)
(23,26)(27,29);;
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, 
s1*s2*s1*s2, s0*s3*s0*s3, s1*s3*s1*s3, 
s0*s1*s0*s1*s0*s1*s0*s1*s0*s1, s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3 ];;
poly := F / rels;;

Permutation Representation (Magma) :

s0 := Sym(29)!(2,3)(4,5);
s1 := Sym(29)!(1,2)(3,4);
s2 := Sym(29)!( 7, 8)( 9,10)(11,14)(12,16)(13,15)(17,20)(18,22)(19,21)(24,27)
(25,26)(28,29);
s3 := Sym(29)!( 6,12)( 7, 9)( 8,18)(10,13)(11,15)(14,24)(16,19)(17,21)(20,28)
(22,25)(23,26)(27,29);
poly := sub<Sym(29)|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, s1*s2*s1*s2, s0*s3*s0*s3, 
s1*s3*s1*s3, s0*s1*s0*s1*s0*s1*s0*s1*s0*s1, 
s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3 >;

to this polytope