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

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {2,6,6,2}*864a
if this polytope has a name.
Group : SmallGroup(864,4033)
Rank : 5
Schlafli Type : {2,6,6,2}
Number of vertices, edges, etc : 2, 18, 54, 18, 2
Order of s0s1s2s3s4 : 6
Order of s0s1s2s3s4s3s2s1 : 2
Special Properties :
   Degenerate
   Universal
   Orientable
   Flat
Related Polytopes :
   Facet
   Vertex Figure
   Dual
Facet Of :
   {2,6,6,2,2} of size 1728
Vertex Figure Of :
   {2,2,6,6,2} of size 1728
Quotients (Maximal Quotients in Boldface) :
   2-fold quotients : {2,6,3,2}*432
   3-fold quotients : {2,6,6,2}*288b
   6-fold quotients : {2,6,3,2}*144
   9-fold quotients : {2,2,6,2}*96
   18-fold quotients : {2,2,3,2}*48
   27-fold quotients : {2,2,2,2}*32
Covers (Minimal Covers in Boldface) :
   2-fold covers : {2,6,12,2}*1728a, {2,6,6,4}*1728a, {2,12,6,2}*1728c, {4,6,6,2}*1728c
Permutation Representation (GAP) :
s0 := (1,2);;
s1 := ( 4, 5)( 7, 8)(10,11)(13,14)(16,17)(19,20);;
s2 := ( 6,10)( 7,11)( 8, 9)(15,19)(16,20)(17,18);;
s3 := ( 3,15)( 4,16)( 5,17)( 6,12)( 7,13)( 8,14)( 9,18)(10,19)(11,20);;
s4 := (21,22);;
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, 
s0*s4*s0*s4, s1*s4*s1*s4, s2*s4*s2*s4, 
s3*s4*s3*s4, s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2, 
s1*s2*s3*s2*s3*s2*s1*s2*s3*s2*s3*s2, 
s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3, 
s1*s2*s3*s2*s1*s2*s1*s2*s3*s2*s1*s2*s3*s1*s2*s1*s3*s2 ];;
poly := F / rels;;
 
Permutation Representation (Magma) :
s0 := Sym(22)!(1,2);
s1 := Sym(22)!( 4, 5)( 7, 8)(10,11)(13,14)(16,17)(19,20);
s2 := Sym(22)!( 6,10)( 7,11)( 8, 9)(15,19)(16,20)(17,18);
s3 := Sym(22)!( 3,15)( 4,16)( 5,17)( 6,12)( 7,13)( 8,14)( 9,18)(10,19)(11,20);
s4 := Sym(22)!(21,22);
poly := sub<Sym(22)|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, s0*s4*s0*s4, 
s1*s4*s1*s4, s2*s4*s2*s4, s3*s4*s3*s4, 
s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2, 
s1*s2*s3*s2*s3*s2*s1*s2*s3*s2*s3*s2, 
s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3, 
s1*s2*s3*s2*s1*s2*s1*s2*s3*s2*s1*s2*s3*s1*s2*s1*s3*s2 >; 
 

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