Polytope of Type {9,2,4,12}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {9,2,4,12}*1728a
if this polytope has a name.
Group : SmallGroup(1728,14460)
Rank : 5
Schlafli Type : {9,2,4,12}
Number of vertices, edges, etc : 9, 9, 4, 24, 12
Order of s₀s₁s₂s₃s₄ : 36
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 : {9,2,2,12}*864, {9,2,4,6}*864a
   3-fold quotients : {9,2,4,4}*576, {3,2,4,12}*576a
   4-fold quotients : {9,2,2,6}*432
   6-fold quotients : {9,2,2,4}*288, {9,2,4,2}*288, {3,2,2,12}*288, {3,2,4,6}*288a
   8-fold quotients : {9,2,2,3}*216
   9-fold quotients : {3,2,4,4}*192
   12-fold quotients : {9,2,2,2}*144, {3,2,2,6}*144
   18-fold quotients : {3,2,2,4}*96, {3,2,4,2}*96
   24-fold quotients : {3,2,2,3}*72
   36-fold quotients : {3,2,2,2}*48
Covers (Minimal Covers in Boldface) :
   None in this atlas.
Permutation Representation (GAP) :

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