Polytope of Type {4,6,2,10}
This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {4,6,2,10}*960b
if this polytope has a name.
Group : SmallGroup(960,11372)
Rank : 5
Schlafli Type : {4,6,2,10}
Number of vertices, edges, etc : 4, 12, 6, 10, 10
Order of s0s1s2s3s4 : 30
Order of s0s1s2s3s4s3s2s1 : 2
Special Properties :
Degenerate
Universal
Non-Orientable
Flat
Related Polytopes :
Facet
Vertex Figure
Dual
Facet Of :
{4,6,2,10,2} of size 1920
Vertex Figure Of :
{2,4,6,2,10} of size 1920
Quotients (Maximal Quotients in Boldface) :
2-fold quotients : {4,3,2,10}*480, {4,6,2,5}*480b
4-fold quotients : {4,3,2,5}*240
5-fold quotients : {4,6,2,2}*192b
10-fold quotients : {4,3,2,2}*96
Covers (Minimal Covers in Boldface) :
2-fold covers : {4,6,2,20}*1920b, {4,6,2,10}*1920
Permutation Representation (GAP) :
s0 := (4,6);;
s1 := (3,4)(5,6);;
s2 := (1,3)(2,5)(4,6);;
s3 := ( 9,10)(11,12)(13,14)(15,16);;
s4 := ( 7,11)( 8, 9)(10,15)(12,13)(14,16);;
poly := Group([s0,s1,s2,s3,s4]);;
Finitely Presented Group Representation (GAP) :
F := FreeGroup("s0","s1","s2","s3","s4");;
s0 := F.1;; s1 := F.2;; s2 := F.3;; s3 := F.4;; s4 := F.5;;
rels := [ s0*s0, s1*s1, s2*s2, s3*s3, s4*s4, s0*s2*s0*s2,
s0*s3*s0*s3, s1*s3*s1*s3, s2*s3*s2*s3,
s0*s4*s0*s4, s1*s4*s1*s4, s2*s4*s2*s4,
s0*s1*s0*s1*s0*s1*s0*s1, s0*s1*s2*s0*s1*s2*s0*s1*s2,
s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4 ];;
poly := F / rels;;
Permutation Representation (Magma) :
s0 := Sym(16)!(4,6);
s1 := Sym(16)!(3,4)(5,6);
s2 := Sym(16)!(1,3)(2,5)(4,6);
s3 := Sym(16)!( 9,10)(11,12)(13,14)(15,16);
s4 := Sym(16)!( 7,11)( 8, 9)(10,15)(12,13)(14,16);
poly := sub<Sym(16)|s0,s1,s2,s3,s4>;
Finitely Presented Group Representation (Magma) :
poly<s0,s1,s2,s3,s4> := Group< s0,s1,s2,s3,s4 | s0*s0, s1*s1, s2*s2,
s3*s3, s4*s4, s0*s2*s0*s2, s0*s3*s0*s3,
s1*s3*s1*s3, s2*s3*s2*s3, s0*s4*s0*s4,
s1*s4*s1*s4, s2*s4*s2*s4, s0*s1*s0*s1*s0*s1*s0*s1,
s0*s1*s2*s0*s1*s2*s0*s1*s2, s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4 >;
to this polytope