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

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {12,4,2,9}*1728a
if this polytope has a name.
Group : SmallGroup(1728,14460)
Rank : 5
Schlafli Type : {12,4,2,9}
Number of vertices, edges, etc : 12, 24, 4, 9, 9
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 : {12,2,2,9}*864, {6,4,2,9}*864a
   3-fold quotients : {4,4,2,9}*576, {12,4,2,3}*576a
   4-fold quotients : {6,2,2,9}*432
   6-fold quotients : {2,4,2,9}*288, {4,2,2,9}*288, {12,2,2,3}*288, {6,4,2,3}*288a
   8-fold quotients : {3,2,2,9}*216
   9-fold quotients : {4,4,2,3}*192
   12-fold quotients : {2,2,2,9}*144, {6,2,2,3}*144
   18-fold quotients : {2,4,2,3}*96, {4,2,2,3}*96
   24-fold quotients : {3,2,2,3}*72
   36-fold quotients : {2,2,2,3}*48
Covers (Minimal Covers in Boldface) :
   None in this atlas.
Permutation Representation (GAP) :
s0 := ( 2, 3)( 4, 5)( 6,10)( 8,12)( 9,11)(15,20)(16,19)(17,18)(21,22)(23,24);;
s1 := ( 1, 8)( 2, 4)( 3,17)( 5, 9)( 6,23)( 7,11)(10,21)(12,18)(13,19)(14,15)
(16,24)(20,22);;
s2 := ( 2, 6)( 3,10)( 8,15)( 9,16)(11,19)(12,20);;
s3 := (26,27)(28,29)(30,31)(32,33);;
s4 := (25,26)(27,28)(29,30)(31,32);;
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, 
s0*s3*s0*s3, s1*s3*s1*s3, s2*s3*s2*s3, 
s0*s4*s0*s4, s1*s4*s1*s4, s2*s4*s2*s4, 
s0*s1*s2*s1*s0*s1*s2*s1, 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, 
s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1 ];;
poly := F / rels;;
 
Permutation Representation (Magma) :
s0 := Sym(33)!( 2, 3)( 4, 5)( 6,10)( 8,12)( 9,11)(15,20)(16,19)(17,18)(21,22)
(23,24);
s1 := Sym(33)!( 1, 8)( 2, 4)( 3,17)( 5, 9)( 6,23)( 7,11)(10,21)(12,18)(13,19)
(14,15)(16,24)(20,22);
s2 := Sym(33)!( 2, 6)( 3,10)( 8,15)( 9,16)(11,19)(12,20);
s3 := Sym(33)!(26,27)(28,29)(30,31)(32,33);
s4 := Sym(33)!(25,26)(27,28)(29,30)(31,32);
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, s0*s3*s0*s3, 
s1*s3*s1*s3, s2*s3*s2*s3, s0*s4*s0*s4, 
s1*s4*s1*s4, s2*s4*s2*s4, s0*s1*s2*s1*s0*s1*s2*s1, 
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, 
s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1 >; 
 

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