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Polytope of Type {6,3,4,2,6}
This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {6,3,4,2,6}*1728
if this polytope has a name.
Group : SmallGroup(1728,47874)
Rank : 6
Schlafli Type : {6,3,4,2,6}
Number of vertices, edges, etc : 6, 9, 6, 4, 6, 6
Order of s0s1s2s3s4s5 : 6
Order of s0s1s2s3s4s5s4s3s2s1 : 2
Special Properties :
Degenerate
Universal
Non-Orientable
Flat
Related Polytopes :
Facet
Vertex Figure
Dual
Facet Of :
None in this Atlas
Vertex Figure Of :
None in this Atlas
Quotients (Maximal Quotients in Boldface) :
2-fold quotients : {6,3,4,2,3}*864
3-fold quotients : {2,3,4,2,6}*576, {6,3,4,2,2}*576
6-fold quotients : {2,3,4,2,3}*288
9-fold quotients : {2,3,4,2,2}*192
Covers (Minimal Covers in Boldface) :
None in this atlas.
Permutation Representation (GAP) :
s0 := ( 5, 9)( 6,10)( 7,11)( 8,12);;
s1 := ( 1, 5)( 2, 6)( 3, 8)( 4, 7)(11,12);;
s2 := ( 2, 3)( 5, 9)( 6,11)( 7,10)( 8,12);;
s3 := ( 1, 2)( 3, 4)( 5, 6)( 7, 8)( 9,10)(11,12);;
s4 := (15,16)(17,18);;
s5 := (13,17)(14,15)(16,18);;
poly := Group([s0,s1,s2,s3,s4,s5]);;
Finitely Presented Group Representation (GAP) :
F := FreeGroup("s0","s1","s2","s3","s4","s5");;
s0 := F.1;; s1 := F.2;; s2 := F.3;; s3 := F.4;; s4 := F.5;; s5 := F.6;;
rels := [ s0*s0, s1*s1, s2*s2, s3*s3, s4*s4, s5*s5,
s0*s2*s0*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, s1*s2*s1*s2*s1*s2,
s2*s3*s2*s3*s2*s3*s2*s3, s1*s3*s2*s1*s3*s2*s1*s3*s2,
s2*s0*s1*s0*s1*s2*s0*s1*s0*s1, s4*s5*s4*s5*s4*s5*s4*s5*s4*s5*s4*s5 ];;
poly := F / rels;;
Permutation Representation (Magma) :
s0 := Sym(18)!( 5, 9)( 6,10)( 7,11)( 8,12);
s1 := Sym(18)!( 1, 5)( 2, 6)( 3, 8)( 4, 7)(11,12);
s2 := Sym(18)!( 2, 3)( 5, 9)( 6,11)( 7,10)( 8,12);
s3 := Sym(18)!( 1, 2)( 3, 4)( 5, 6)( 7, 8)( 9,10)(11,12);
s4 := Sym(18)!(15,16)(17,18);
s5 := Sym(18)!(13,17)(14,15)(16,18);
poly := sub<Sym(18)|s0,s1,s2,s3,s4,s5>;
Finitely Presented Group Representation (Magma) :
poly<s0,s1,s2,s3,s4,s5> := Group< s0,s1,s2,s3,s4,s5 | s0*s0, s1*s1, s2*s2,
s3*s3, s4*s4, s5*s5, s0*s2*s0*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,
s1*s2*s1*s2*s1*s2, s2*s3*s2*s3*s2*s3*s2*s3,
s1*s3*s2*s1*s3*s2*s1*s3*s2, s2*s0*s1*s0*s1*s2*s0*s1*s0*s1,
s4*s5*s4*s5*s4*s5*s4*s5*s4*s5*s4*s5 >;
to this polytope