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

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {4,2,6,6}*1728b
if this polytope has a name.
Group : SmallGroup(1728,30804)
Rank : 5
Schlafli Type : {4,2,6,6}
Number of vertices, edges, etc : 4, 4, 18, 54, 18
Order of s0s1s2s3s4 : 12
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 : {4,2,6,6}*864, {2,2,6,6}*864b
   3-fold quotients : {4,2,6,6}*576a
   4-fold quotients : {2,2,6,6}*432
   6-fold quotients : {2,2,6,6}*288a
   9-fold quotients : {4,2,2,6}*192, {4,2,6,2}*192
   18-fold quotients : {4,2,2,3}*96, {4,2,3,2}*96, {2,2,2,6}*96, {2,2,6,2}*96
   27-fold quotients : {4,2,2,2}*64
   36-fold quotients : {2,2,2,3}*48, {2,2,3,2}*48
   54-fold quotients : {2,2,2,2}*32
Covers (Minimal Covers in Boldface) :
   None in this atlas.
Permutation Representation (GAP) :
s0 := (2,3);;
s1 := (1,2)(3,4);;
s2 := ( 6, 7)( 9,10)(12,13)(15,16)(18,19)(21,22);;
s3 := ( 8,12)( 9,13)(10,11)(17,21)(18,22)(19,20);;
s4 := ( 5,17)( 6,19)( 7,18)( 8,14)( 9,16)(10,15)(11,20)(12,22)(13,21);;
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, 
s0*s1*s0*s1*s0*s1*s0*s1, s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3, 
s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4, 
s4*s2*s3*s4*s2*s3*s2*s3*s4*s2*s3*s4*s2*s3*s2*s3, 
s2*s3*s4*s3*s2*s3*s4*s3*s4*s3*s2*s3*s4*s3*s2*s3 ];;
poly := F / rels;;
 
Permutation Representation (Magma) :
s0 := Sym(22)!(2,3);
s1 := Sym(22)!(1,2)(3,4);
s2 := Sym(22)!( 6, 7)( 9,10)(12,13)(15,16)(18,19)(21,22);
s3 := Sym(22)!( 8,12)( 9,13)(10,11)(17,21)(18,22)(19,20);
s4 := Sym(22)!( 5,17)( 6,19)( 7,18)( 8,14)( 9,16)(10,15)(11,20)(12,22)(13,21);
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*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, s0*s1*s0*s1*s0*s1*s0*s1, 
s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3, 
s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4, 
s4*s2*s3*s4*s2*s3*s2*s3*s4*s2*s3*s4*s2*s3*s2*s3, 
s2*s3*s4*s3*s2*s3*s4*s3*s4*s3*s2*s3*s4*s3*s2*s3 >; 
 

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