Polytope of Type {2,9,2,24}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {2,9,2,24}*1728
if this polytope has a name.
Group : SmallGroup(1728,15830)
Rank : 5
Schlafli Type : {2,9,2,24}
Number of vertices, edges, etc : 2, 9, 9, 24, 24
Order of s₀s₁s₂s₃s₄ : 72
Order of s₀s₁s₂s₃s₄s₃s₂s₁ : 2
Special Properties :
   Degenerate
   Universal
   Orientable
   Flat
Related Polytopes :
   Facet
   Vertex Figure
   Dual
Facet Of :
   None in this Atlas
Vertex Figure Of :
   None in this Atlas
Quotients (Maximal Quotients in Boldface) :
   2-fold quotients : {2,9,2,12}*864
   3-fold quotients : {2,9,2,8}*576, {2,3,2,24}*576
   4-fold quotients : {2,9,2,6}*432
   6-fold quotients : {2,9,2,4}*288, {2,3,2,12}*288
   8-fold quotients : {2,9,2,3}*216
   9-fold quotients : {2,3,2,8}*192
   12-fold quotients : {2,9,2,2}*144, {2,3,2,6}*144
   18-fold quotients : {2,3,2,4}*96
   24-fold quotients : {2,3,2,3}*72
   36-fold quotients : {2,3,2,2}*48
Covers (Minimal Covers in Boldface) :
   None in this atlas.
Permutation Representation (GAP) :

s0 := (1,2);;
s1 := ( 4, 5)( 6, 7)( 8, 9)(10,11);;
s2 := ( 3, 4)( 5, 6)( 7, 8)( 9,10);;
s3 := (13,14)(15,16)(17,20)(18,22)(19,21)(23,26)(24,28)(25,27)(30,33)(31,32)
(34,35);;
s4 := (12,18)(13,15)(14,24)(16,19)(17,21)(20,30)(22,25)(23,27)(26,34)(28,31)
(29,32)(33,35);;
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*s1*s0*s1, 
s0*s2*s0*s2, s0*s3*s0*s3, s1*s3*s1*s3, 
s2*s3*s2*s3, s0*s4*s0*s4, s1*s4*s1*s4, 
s2*s4*s2*s4, s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2, 
s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4 ];;
poly := F / rels;;

Permutation Representation (Magma) :

s0 := Sym(35)!(1,2);
s1 := Sym(35)!( 4, 5)( 6, 7)( 8, 9)(10,11);
s2 := Sym(35)!( 3, 4)( 5, 6)( 7, 8)( 9,10);
s3 := Sym(35)!(13,14)(15,16)(17,20)(18,22)(19,21)(23,26)(24,28)(25,27)(30,33)
(31,32)(34,35);
s4 := Sym(35)!(12,18)(13,15)(14,24)(16,19)(17,21)(20,30)(22,25)(23,27)(26,34)
(28,31)(29,32)(33,35);
poly := sub<Sym(35)|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*s1*s0*s1, s0*s2*s0*s2, 
s0*s3*s0*s3, s1*s3*s1*s3, s2*s3*s2*s3, 
s0*s4*s0*s4, s1*s4*s1*s4, s2*s4*s2*s4, 
s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2, 
s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4 >;

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