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Polytope of Type {6,2,3,2,2,3}
This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {6,2,3,2,2,3}*864
if this polytope has a name.
Group : SmallGroup(864,4704)
Rank : 7
Schlafli Type : {6,2,3,2,2,3}
Number of vertices, edges, etc : 6, 6, 3, 3, 2, 3, 3
Order of s0s1s2s3s4s5s6 : 6
Order of s0s1s2s3s4s5s6s5s4s3s2s1 : 2
Special Properties :
Degenerate
Universal
Orientable
Flat
Related Polytopes :
Facet
Vertex Figure
Dual
Facet Of :
{6,2,3,2,2,3,2} of size 1728
Vertex Figure Of :
{2,6,2,3,2,2,3} of size 1728
Quotients (Maximal Quotients in Boldface) :
2-fold quotients : {3,2,3,2,2,3}*432
3-fold quotients : {2,2,3,2,2,3}*288
Covers (Minimal Covers in Boldface) :
2-fold covers : {12,2,3,2,2,3}*1728, {6,2,3,2,2,6}*1728, {6,2,6,2,2,3}*1728
Permutation Representation (GAP) :
s0 := (3,4)(5,6);;
s1 := (1,5)(2,3)(4,6);;
s2 := (8,9);;
s3 := (7,8);;
s4 := (10,11);;
s5 := (13,14);;
s6 := (12,13);;
poly := Group([s0,s1,s2,s3,s4,s5,s6]);;
Finitely Presented Group Representation (GAP) :
F := FreeGroup("s0","s1","s2","s3","s4","s5","s6");;
s0 := F.1;; s1 := F.2;; s2 := F.3;; s3 := F.4;; s4 := F.5;; s5 := F.6;; s6 := F.7;;
rels := [ s0*s0, s1*s1, s2*s2, s3*s3, s4*s4, s5*s5,
s6*s6, s0*s2*s0*s2, s1*s2*s1*s2, s0*s3*s0*s3,
s1*s3*s1*s3, s0*s4*s0*s4, s1*s4*s1*s4,
s2*s4*s2*s4, s3*s4*s3*s4, s0*s5*s0*s5,
s1*s5*s1*s5, s2*s5*s2*s5, s3*s5*s3*s5,
s4*s5*s4*s5, s0*s6*s0*s6, s1*s6*s1*s6,
s2*s6*s2*s6, s3*s6*s3*s6, s4*s6*s4*s6,
s2*s3*s2*s3*s2*s3, s5*s6*s5*s6*s5*s6,
s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1 ];;
poly := F / rels;;
Permutation Representation (Magma) :
s0 := Sym(14)!(3,4)(5,6);
s1 := Sym(14)!(1,5)(2,3)(4,6);
s2 := Sym(14)!(8,9);
s3 := Sym(14)!(7,8);
s4 := Sym(14)!(10,11);
s5 := Sym(14)!(13,14);
s6 := Sym(14)!(12,13);
poly := sub<Sym(14)|s0,s1,s2,s3,s4,s5,s6>;
Finitely Presented Group Representation (Magma) :
poly<s0,s1,s2,s3,s4,s5,s6> := Group< s0,s1,s2,s3,s4,s5,s6 | s0*s0, s1*s1, s2*s2,
s3*s3, s4*s4, s5*s5, s6*s6, s0*s2*s0*s2,
s1*s2*s1*s2, s0*s3*s0*s3, s1*s3*s1*s3,
s0*s4*s0*s4, s1*s4*s1*s4, s2*s4*s2*s4,
s3*s4*s3*s4, s0*s5*s0*s5, s1*s5*s1*s5,
s2*s5*s2*s5, s3*s5*s3*s5, s4*s5*s4*s5,
s0*s6*s0*s6, s1*s6*s1*s6, s2*s6*s2*s6,
s3*s6*s3*s6, s4*s6*s4*s6, s2*s3*s2*s3*s2*s3,
s5*s6*s5*s6*s5*s6, s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1 >;
to this polytope