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Polytope of Type {2,8,6}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {2,8,6}*384c
if this polytope has a name.
Group : SmallGroup(384,20070)
Rank : 4
Schlafli Type : {2,8,6}
Number of vertices, edges, etc : 2, 16, 48, 12
Order of s0s1s2s3 : 6
Order of s0s1s2s3s2s1 : 2
Special Properties :
   Degenerate
   Universal
   Orientable
   Flat
Related Polytopes :
   Facet
   Vertex Figure
   Dual
Facet Of :
   {2,8,6,2} of size 768
Vertex Figure Of :
   {2,2,8,6} of size 768
   {3,2,8,6} of size 1152
   {5,2,8,6} of size 1920
Quotients (Maximal Quotients in Boldface) :
   2-fold quotients : {2,4,6}*192
   4-fold quotients : {2,4,3}*96, {2,4,6}*96b, {2,4,6}*96c
   8-fold quotients : {2,4,3}*48, {2,2,6}*48
   16-fold quotients : {2,2,3}*24
   24-fold quotients : {2,2,2}*16
Covers (Minimal Covers in Boldface) :
   2-fold covers : {2,8,12}*768f, {2,8,6}*768f, {2,8,12}*768g, {4,8,6}*768d
   3-fold covers : {2,8,18}*1152c, {2,24,6}*1152c, {2,24,6}*1152d, {6,8,6}*1152c
   5-fold covers : {2,40,6}*1920b, {10,8,6}*1920b, {2,8,30}*1920c
Permutation Representation (GAP) :
s0 := (1,2);;
s1 := ( 3,13)( 4,14)( 5,12)( 6,11)( 7,17)( 8,18)( 9,16)(10,15);;
s2 := ( 5, 7)( 6, 8)( 9,10)(13,15)(14,16)(17,18);;
s3 := ( 5, 6)( 7, 9)( 8,10)(11,12)(15,18)(16,17);;
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*s1*s0*s1, 
s0*s2*s0*s2, s0*s3*s0*s3, s1*s3*s1*s3, 
s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3, 
s3*s1*s2*s3*s2*s1*s2*s3*s2*s3*s1*s2*s1*s2 ];;
poly := F / rels;;
 
Permutation Representation (Magma) :
s0 := Sym(18)!(1,2);
s1 := Sym(18)!( 3,13)( 4,14)( 5,12)( 6,11)( 7,17)( 8,18)( 9,16)(10,15);
s2 := Sym(18)!( 5, 7)( 6, 8)( 9,10)(13,15)(14,16)(17,18);
s3 := Sym(18)!( 5, 6)( 7, 9)( 8,10)(11,12)(15,18)(16,17);
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*s1*s0*s1, s0*s2*s0*s2, s0*s3*s0*s3, 
s1*s3*s1*s3, s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3, 
s3*s1*s2*s3*s2*s1*s2*s3*s2*s3*s1*s2*s1*s2 >; 
 

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