Polytope of Type {6,6,5}
This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {6,6,5}*1440b
if this polytope has a name.
Group : SmallGroup(1440,5853)
Rank : 4
Schlafli Type : {6,6,5}
Number of vertices, edges, etc : 6, 72, 60, 20
Order of s0s1s2s3 : 30
Order of s0s1s2s3s2s1 : 2
Special Properties :
Universal
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 : {6,6,5}*720b
3-fold quotients : {2,6,5}*480b
6-fold quotients : {2,3,5}*240, {2,6,5}*240b, {2,6,5}*240c
12-fold quotients : {2,3,5}*120
Covers (Minimal Covers in Boldface) :
None in this atlas.
Permutation Representation (GAP) :
s0 := (12,16)(13,15);;
s1 := ( 3, 6)( 4, 5)( 7,10)( 8, 9)(11,12)(13,16)(14,15);;
s2 := ( 1, 4)( 2, 3)( 5, 6)( 7, 9)( 8,10);;
s3 := ( 1, 2)( 3, 8)( 4, 7)( 5,10)( 6, 9);;
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*s2*s1*s0*s1*s2*s1,
s2*s3*s2*s3*s2*s3*s2*s3*s2*s3, s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1,
s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2,
s1*s2*s3*s2*s1*s2*s1*s2*s3*s2*s1*s2 ];;
poly := F / rels;;
Permutation Representation (Magma) :
s0 := Sym(16)!(12,16)(13,15);
s1 := Sym(16)!( 3, 6)( 4, 5)( 7,10)( 8, 9)(11,12)(13,16)(14,15);
s2 := Sym(16)!( 1, 4)( 2, 3)( 5, 6)( 7, 9)( 8,10);
s3 := Sym(16)!( 1, 2)( 3, 8)( 4, 7)( 5,10)( 6, 9);
poly := sub<Sym(16)|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*s2*s1*s0*s1*s2*s1, s2*s3*s2*s3*s2*s3*s2*s3*s2*s3,
s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1,
s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2,
s1*s2*s3*s2*s1*s2*s1*s2*s3*s2*s1*s2 >;
References : None.
to this polytope