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Polytope of Type {2,6,6}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {2,6,6}*240
if this polytope has a name.
Group : SmallGroup(240,189)
Rank : 4
Schlafli Type : {2,6,6}
Number of vertices, edges, etc : 2, 10, 30, 10
Order of s0s1s2s3 : 6
Order of s0s1s2s3s2s1 : 2
Special Properties :
   Degenerate
   Universal
   Non-Orientable
   Flat
Related Polytopes :
   Facet
   Vertex Figure
   Dual
Facet Of :
   {2,6,6,2} of size 480
Vertex Figure Of :
   {2,2,6,6} of size 480
   {3,2,6,6} of size 720
   {4,2,6,6} of size 960
   {5,2,6,6} of size 1200
   {6,2,6,6} of size 1440
   {7,2,6,6} of size 1680
   {8,2,6,6} of size 1920
Quotients (Maximal Quotients in Boldface) :
   No Regular Quotients.
Covers (Minimal Covers in Boldface) :
   2-fold covers : {2,6,6}*480a, {2,6,6}*480b, {2,6,6}*480c
   4-fold covers : {4,6,6}*960, {2,6,12}*960a, {2,6,12}*960b, {2,12,6}*960a, {2,12,6}*960b, {2,6,6}*960
   6-fold covers : {2,6,6}*1440b, {2,6,6}*1440c, {2,6,6}*1440d, {6,6,6}*1440b
   8-fold covers : {4,12,6}*1920a, {4,12,6}*1920b, {2,6,24}*1920a, {2,6,24}*1920b, {2,24,6}*1920a, {2,24,6}*1920b, {8,6,6}*1920, {2,6,12}*1920a, {2,12,6}*1920a, {4,6,6}*1920a, {2,6,24}*1920c, {2,6,24}*1920d, {2,24,6}*1920c, {2,24,6}*1920d, {2,6,6}*1920, {2,6,12}*1920b, {2,12,6}*1920b
Permutation Representation (GAP) :
s0 := (1,2);;
s1 := (4,5)(6,7);;
s2 := (3,4);;
s3 := (4,6)(5,7);;
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, 
s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2, 
s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3, 
s1*s2*s3*s2*s1*s2*s1*s2*s3*s1*s2*s1*s2, 
s3*s2*s1*s3*s2*s3*s2*s3*s2*s1*s2*s3*s2 ];;
poly := F / rels;;
 
Permutation Representation (Magma) :
s0 := Sym(7)!(1,2);
s1 := Sym(7)!(4,5)(6,7);
s2 := Sym(7)!(3,4);
s3 := Sym(7)!(4,6)(5,7);
poly := sub<Sym(7)|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, s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2, 
s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3, 
s1*s2*s3*s2*s1*s2*s1*s2*s3*s1*s2*s1*s2, 
s3*s2*s1*s3*s2*s3*s2*s3*s2*s1*s2*s3*s2 >; 
 

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