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Polytope of Type {4,6,2}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {4,6,2}*864b
if this polytope has a name.
Group : SmallGroup(864,4686)
Rank : 4
Schlafli Type : {4,6,2}
Number of vertices, edges, etc : 36, 108, 54, 2
Order of s0s1s2s3 : 12
Order of s0s1s2s3s2s1 : 2
Special Properties :
   Degenerate
   Universal
   Orientable
   Flat
Related Polytopes :
   Facet
   Vertex Figure
   Dual
Facet Of :
   {4,6,2,2} of size 1728
Vertex Figure Of :
   {2,4,6,2} of size 1728
Quotients (Maximal Quotients in Boldface) :
   3-fold quotients : {4,6,2}*288
   6-fold quotients : {4,6,2}*144
   9-fold quotients : {4,6,2}*96a
   18-fold quotients : {2,6,2}*48
   27-fold quotients : {4,2,2}*32
   36-fold quotients : {2,3,2}*24
   54-fold quotients : {2,2,2}*16
Covers (Minimal Covers in Boldface) :
   2-fold covers : {4,12,2}*1728c, {8,6,2}*1728b, {4,6,4}*1728c
Permutation Representation (GAP) :
s0 := (4,7)(5,8)(6,9);;
s1 := ( 1,10)( 2,12)( 3,11)( 4,13)( 5,15)( 6,14)( 7,16)( 8,18)( 9,17);;
s2 := ( 1, 2)( 4, 8)( 5, 7)( 6, 9)(10,17)(11,16)(12,18)(13,14);;
s3 := (19,20);;
poly := Group([s0,s1,s2,s3]);;
 
Finitely Presented Group Representation (GAP) :
F := FreeGroup("s0","s1","s2","s3");;
s0 := F.1;;  s1 := F.2;;  s2 := F.3;;  s3 := F.4;;  
rels := [ s0*s0, s1*s1, s2*s2, s3*s3, s0*s2*s0*s2, 
s0*s3*s0*s3, s1*s3*s1*s3, s2*s3*s2*s3, 
s0*s1*s0*s1*s0*s1*s0*s1, s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2, 
s2*s0*s1*s2*s1*s0*s1*s2*s1*s2*s0*s1*s2*s1*s0*s1*s2*s1 ];;
poly := F / rels;;
 
Permutation Representation (Magma) :
s0 := Sym(20)!(4,7)(5,8)(6,9);
s1 := Sym(20)!( 1,10)( 2,12)( 3,11)( 4,13)( 5,15)( 6,14)( 7,16)( 8,18)( 9,17);
s2 := Sym(20)!( 1, 2)( 4, 8)( 5, 7)( 6, 9)(10,17)(11,16)(12,18)(13,14);
s3 := Sym(20)!(19,20);
poly := sub<Sym(20)|s0,s1,s2,s3>;
 
Finitely Presented Group Representation (Magma) :
poly<s0,s1,s2,s3> := Group< s0,s1,s2,s3 | s0*s0, s1*s1, s2*s2, 
s3*s3, s0*s2*s0*s2, s0*s3*s0*s3, s1*s3*s1*s3, 
s2*s3*s2*s3, s0*s1*s0*s1*s0*s1*s0*s1, 
s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2, 
s2*s0*s1*s2*s1*s0*s1*s2*s1*s2*s0*s1*s2*s1*s0*s1*s2*s1 >; 
 

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