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Polytope of Type {2,6,12}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {2,6,12}*960b
if this polytope has a name.
Group : SmallGroup(960,10882)
Rank : 4
Schlafli Type : {2,6,12}
Number of vertices, edges, etc : 2, 20, 120, 40
Order of s0s1s2s3 : 12
Order of s0s1s2s3s2s1 : 2
Special Properties :
   Degenerate
   Universal
   Non-Orientable
   Flat
Related Polytopes :
   Facet
   Vertex Figure
   Dual
Facet Of :
   {2,6,12,2} of size 1920
Vertex Figure Of :
   {2,2,6,12} of size 1920
Quotients (Maximal Quotients in Boldface) :
   2-fold quotients : {2,6,6}*480a
   4-fold quotients : {2,6,6}*240
Covers (Minimal Covers in Boldface) :
   2-fold covers : {2,6,12}*1920a, {2,6,24}*1920c, {2,6,24}*1920d
Permutation Representation (GAP) :
s0 := (1,2);;
s1 := ( 3, 4)( 5, 6)( 8, 9)(10,11);;
s2 := (5,6)(7,8);;
s3 := ( 3, 5)( 4, 6)( 8,10)( 9,11);;
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, 
s1*s2*s3*s2*s1*s2*s1*s2*s3*s1*s2*s1*s2, 
s3*s1*s2*s3*s2*s3*s2*s3*s1*s2*s3*s1*s2*s3*s2*s3*s2*s3*s1*s2 ];;
poly := F / rels;;
 
Permutation Representation (Magma) :
s0 := Sym(11)!(1,2);
s1 := Sym(11)!( 3, 4)( 5, 6)( 8, 9)(10,11);
s2 := Sym(11)!(5,6)(7,8);
s3 := Sym(11)!( 3, 5)( 4, 6)( 8,10)( 9,11);
poly := sub<Sym(11)|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, 
s1*s2*s3*s2*s1*s2*s1*s2*s3*s1*s2*s1*s2, 
s3*s1*s2*s3*s2*s3*s2*s3*s1*s2*s3*s1*s2*s3*s2*s3*s2*s3*s1*s2 >; 
 

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