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