Polytope of Type {4,6,3}
This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {4,6,3}*1440c
Also Known As : {{4,6}5,{6,3}4}. Tell me
if this polytope has another name.
Group : SmallGroup(1440,5842)
Rank : 4
Schlafli Type : {4,6,3}
Number of vertices, edges, etc : 30, 120, 90, 6
Order of s0s1s2s3 : 6
Order of s0s1s2s3s2s1 : 6
Special Properties :
Universal
Non-Orientable
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 : {4,6,3}*720
Covers (Minimal Covers in Boldface) :
None in this atlas.
Permutation Representation (GAP) :
s0 := (3,5);;
s1 := (3,4)(5,6)(7,8);;
s2 := (2,4)(7,8);;
s3 := (1,2)(7,8);;
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, s2*s3*s2*s3*s2*s3,
s0*s1*s0*s1*s0*s1*s0*s1, s1*s3*s2*s1*s3*s2*s1*s3*s2*s1*s3*s2,
s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2,
s0*s1*s2*s0*s1*s2*s0*s1*s2*s0*s1*s2*s0*s1*s2 ];;
poly := F / rels;;
Permutation Representation (Magma) :
s0 := Sym(8)!(3,5);
s1 := Sym(8)!(3,4)(5,6)(7,8);
s2 := Sym(8)!(2,4)(7,8);
s3 := Sym(8)!(1,2)(7,8);
poly := sub<Sym(8)|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,
s2*s3*s2*s3*s2*s3, s0*s1*s0*s1*s0*s1*s0*s1,
s1*s3*s2*s1*s3*s2*s1*s3*s2*s1*s3*s2,
s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2,
s0*s1*s2*s0*s1*s2*s0*s1*s2*s0*s1*s2*s0*s1*s2 >;
References : None.
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