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Polytope of Type {6,6,2}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {6,6,2}*384b
if this polytope has a name.
Group : SmallGroup(384,20070)
Rank : 4
Schlafli Type : {6,6,2}
Number of vertices, edges, etc : 16, 48, 16, 2
Order of s0s1s2s3 : 8
Order of s0s1s2s3s2s1 : 2
Special Properties :
   Degenerate
   Universal
   Orientable
   Flat
Related Polytopes :
   Facet
   Vertex Figure
   Dual
Facet Of :
   {6,6,2,2} of size 768
   {6,6,2,3} of size 1152
   {6,6,2,5} of size 1920
Vertex Figure Of :
   {2,6,6,2} of size 768
Quotients (Maximal Quotients in Boldface) :
   2-fold quotients : {6,6,2}*192
   4-fold quotients : {3,6,2}*96, {6,3,2}*96
   8-fold quotients : {3,3,2}*48
   24-fold quotients : {2,2,2}*16
Covers (Minimal Covers in Boldface) :
   2-fold covers : {6,12,2}*768, {12,6,2}*768, {6,6,4}*768e
   3-fold covers : {6,6,2}*1152a, {6,6,2}*1152b, {6,6,6}*1152b
   5-fold covers : {6,30,2}*1920, {30,6,2}*1920, {6,6,10}*1920
Permutation Representation (GAP) :
s0 := ( 3, 5)( 4, 6)( 7, 8)( 9,10)(11,14)(12,13);;
s1 := ( 3, 4)( 5, 7)( 6, 8)(11,12)(13,15)(14,16);;
s2 := ( 1,15)( 2,16)( 3,12)( 4,11)( 5,13)( 6,14)( 7, 9)( 8,10);;
s3 := (17,18);;
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*s0*s1*s0*s1, 
s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2, 
s2*s0*s1*s0*s1*s2*s1*s2*s0*s1*s2*s1*s0*s1 ];;
poly := F / rels;;
 
Permutation Representation (Magma) :
s0 := Sym(18)!( 3, 5)( 4, 6)( 7, 8)( 9,10)(11,14)(12,13);
s1 := Sym(18)!( 3, 4)( 5, 7)( 6, 8)(11,12)(13,15)(14,16);
s2 := Sym(18)!( 1,15)( 2,16)( 3,12)( 4,11)( 5,13)( 6,14)( 7, 9)( 8,10);
s3 := Sym(18)!(17,18);
poly := sub<Sym(18)|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*s0*s1*s0*s1, 
s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2, 
s2*s0*s1*s0*s1*s2*s1*s2*s0*s1*s2*s1*s0*s1 >; 
 

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