Polytope of Type {3,6,2,5}
This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {3,6,2,5}*480
if this polytope has a name.
Group : SmallGroup(480,1193)
Rank : 5
Schlafli Type : {3,6,2,5}
Number of vertices, edges, etc : 4, 12, 8, 5, 5
Order of s0s1s2s3s4 : 20
Order of s0s1s2s3s4s3s2s1 : 2
Special Properties :
Degenerate
Universal
Orientable
Flat
Related Polytopes :
Facet
Vertex Figure
Dual
Facet Of :
{3,6,2,5,2} of size 960
Vertex Figure Of :
{2,3,6,2,5} of size 960
Quotients (Maximal Quotients in Boldface) :
2-fold quotients : {3,3,2,5}*240
Covers (Minimal Covers in Boldface) :
2-fold covers : {3,12,2,5}*960, {3,6,2,10}*960, {6,6,2,5}*960
3-fold covers : {3,6,2,5}*1440, {3,6,2,15}*1440
4-fold covers : {3,6,2,5}*1920, {3,6,2,20}*1920, {3,6,4,10}*1920, {6,12,2,5}*1920a, {12,6,2,5}*1920a, {3,12,2,10}*1920, {6,12,2,5}*1920b, {12,6,2,5}*1920b, {6,6,2,5}*1920b, {6,6,2,10}*1920
Permutation Representation (GAP) :
s0 := (1,4)(2,6);;
s1 := (3,4)(5,6);;
s2 := (1,4)(2,6)(3,5);;
s3 := ( 8, 9)(10,11);;
s4 := ( 7, 8)( 9,10);;
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, s3*s4*s3*s4*s3*s4*s3*s4*s3*s4,
s2*s0*s1*s2*s0*s1*s2*s0*s1*s2*s0*s1 ];;
poly := F / rels;;
Permutation Representation (Magma) :
s0 := Sym(11)!(1,4)(2,6);
s1 := Sym(11)!(3,4)(5,6);
s2 := Sym(11)!(1,4)(2,6)(3,5);
s3 := Sym(11)!( 8, 9)(10,11);
s4 := Sym(11)!( 7, 8)( 9,10);
poly := sub<Sym(11)|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,
s3*s4*s3*s4*s3*s4*s3*s4*s3*s4, s2*s0*s1*s2*s0*s1*s2*s0*s1*s2*s0*s1 >;
to this polytope