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Polytope of Type {3,6,12}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {3,6,12}*960
if this polytope has a name.
Group : SmallGroup(960,10871)
Rank : 4
Schlafli Type : {3,6,12}
Number of vertices, edges, etc : 5, 20, 80, 20
Order of s0s1s2s3 : 20
Order of s0s1s2s3s2s1 : 6
Special Properties :
   Universal
   Orientable
Related Polytopes :
   Facet
   Vertex Figure
   Dual
Facet Of :
   {3,6,12,2} of size 1920
Vertex Figure Of :
   {2,3,6,12} of size 1920
Quotients (Maximal Quotients in Boldface) :
   2-fold quotients : {3,6,6}*480
   4-fold quotients : {3,3,6}*240, {3,6,3}*240
   8-fold quotients : {3,3,3}*120
Covers (Minimal Covers in Boldface) :
   2-fold covers : {3,6,24}*1920, {6,6,12}*1920, {3,12,12}*1920
Permutation Representation (GAP) :
s0 := (7,9);;
s1 := (8,9);;
s2 := (2,3)(6,8);;
s3 := (1,2)(3,4)(5,6);;
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, s0*s1*s0*s1*s0*s1, 
s2*s0*s1*s2*s0*s1*s2*s0*s1*s2*s0*s1, 
s3*s1*s2*s3*s1*s2*s3*s1*s2*s3*s1*s2 ];;
poly := F / rels;;
 
Permutation Representation (Magma) :
s0 := Sym(9)!(7,9);
s1 := Sym(9)!(8,9);
s2 := Sym(9)!(2,3)(6,8);
s3 := Sym(9)!(1,2)(3,4)(5,6);
poly := sub<Sym(9)|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, 
s0*s1*s0*s1*s0*s1, s2*s0*s1*s2*s0*s1*s2*s0*s1*s2*s0*s1, 
s3*s1*s2*s3*s1*s2*s3*s1*s2*s3*s1*s2 >; 
 
References : None.
to this polytope