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Polytope of Type {4,6,2,9}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {4,6,2,9}*864a
if this polytope has a name.
Group : SmallGroup(864,2462)
Rank : 5
Schlafli Type : {4,6,2,9}
Number of vertices, edges, etc : 4, 12, 6, 9, 9
Order of s0s1s2s3s4 : 36
Order of s0s1s2s3s4s3s2s1 : 2
Special Properties :
   Degenerate
   Universal
   Orientable
   Flat
Related Polytopes :
   Facet
   Vertex Figure
   Dual
Facet Of :
   {4,6,2,9,2} of size 1728
Vertex Figure Of :
   {2,4,6,2,9} of size 1728
Quotients (Maximal Quotients in Boldface) :
   2-fold quotients : {2,6,2,9}*432
   3-fold quotients : {4,2,2,9}*288, {4,6,2,3}*288a
   4-fold quotients : {2,3,2,9}*216
   6-fold quotients : {2,2,2,9}*144, {2,6,2,3}*144
   9-fold quotients : {4,2,2,3}*96
   12-fold quotients : {2,3,2,3}*72
   18-fold quotients : {2,2,2,3}*48
Covers (Minimal Covers in Boldface) :
   2-fold covers : {4,12,2,9}*1728a, {8,6,2,9}*1728, {4,6,2,18}*1728a
Permutation Representation (GAP) :
s0 := ( 2, 5)( 6, 9)( 7,10);;
s1 := ( 1, 2)( 3, 7)( 4, 6)( 5, 8)( 9,12)(10,11);;
s2 := ( 1, 3)( 2, 6)( 5, 9)( 8,11);;
s3 := (14,15)(16,17)(18,19)(20,21);;
s4 := (13,14)(15,16)(17,18)(19,20);;
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*s0*s1*s0*s1*s0*s1, s0*s1*s2*s1*s0*s1*s2*s1, 
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 ];;
poly := F / rels;;
 
Permutation Representation (Magma) :
s0 := Sym(21)!( 2, 5)( 6, 9)( 7,10);
s1 := Sym(21)!( 1, 2)( 3, 7)( 4, 6)( 5, 8)( 9,12)(10,11);
s2 := Sym(21)!( 1, 3)( 2, 6)( 5, 9)( 8,11);
s3 := Sym(21)!(14,15)(16,17)(18,19)(20,21);
s4 := Sym(21)!(13,14)(15,16)(17,18)(19,20);
poly := sub<Sym(21)|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*s0*s1*s0*s1*s0*s1, 
s0*s1*s2*s1*s0*s1*s2*s1, 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 >; 
 

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