Polytope of Type {2,6,10}
This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {2,6,10}*480f
if this polytope has a name.
Group : SmallGroup(480,1187)
Rank : 4
Schlafli Type : {2,6,10}
Number of vertices, edges, etc : 2, 12, 60, 20
Order of s0s1s2s3 : 10
Order of s0s1s2s3s2s1 : 2
Special Properties :
Degenerate
Universal
Non-Orientable
Flat
Related Polytopes :
Facet
Vertex Figure
Dual
Facet Of :
{2,6,10,2} of size 960
Vertex Figure Of :
{2,2,6,10} of size 960
{3,2,6,10} of size 1440
{4,2,6,10} of size 1920
Quotients (Maximal Quotients in Boldface) :
2-fold quotients : {2,3,10}*240a, {2,6,5}*240c
4-fold quotients : {2,3,5}*120
Covers (Minimal Covers in Boldface) :
2-fold covers : {2,6,10}*960c
3-fold covers : {2,6,10}*1440c, {2,6,30}*1440b
4-fold covers : {4,6,10}*1920d, {2,6,20}*1920c, {2,12,10}*1920c, {2,6,20}*1920e, {2,12,10}*1920e, {2,6,10}*1920b
Permutation Representation (GAP) :
s0 := (1,2);;
s1 := ( 4, 5)( 6, 7)( 8, 9)(10,11);;
s2 := ( 3, 4)( 6, 7)( 8,10)( 9,11);;
s3 := ( 4, 6)( 5, 7)( 8,11)( 9,10);;
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*s1*s0*s1,
s0*s2*s0*s2, s0*s3*s0*s3, s1*s3*s1*s3,
s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2,
s1*s2*s3*s2*s1*s2*s1*s2*s3*s2*s1*s2,
s1*s2*s3*s1*s2*s3*s1*s2*s3*s1*s2*s3*s1*s2*s3 ];;
poly := F / rels;;
Permutation Representation (Magma) :
s0 := Sym(11)!(1,2);
s1 := Sym(11)!( 4, 5)( 6, 7)( 8, 9)(10,11);
s2 := Sym(11)!( 3, 4)( 6, 7)( 8,10)( 9,11);
s3 := Sym(11)!( 4, 6)( 5, 7)( 8,11)( 9,10);
poly := sub<Sym(11)|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*s1*s0*s1, s0*s2*s0*s2, s0*s3*s0*s3,
s1*s3*s1*s3, s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2,
s1*s2*s3*s2*s1*s2*s1*s2*s3*s2*s1*s2,
s1*s2*s3*s1*s2*s3*s1*s2*s3*s1*s2*s3*s1*s2*s3 >;
to this polytope