Polytope of Type {2,8,2,11}
This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {2,8,2,11}*704
if this polytope has a name.
Group : SmallGroup(704,1204)
Rank : 5
Schlafli Type : {2,8,2,11}
Number of vertices, edges, etc : 2, 8, 8, 11, 11
Order of s0s1s2s3s4 : 88
Order of s0s1s2s3s4s3s2s1 : 2
Special Properties :
Degenerate
Universal
Orientable
Flat
Related Polytopes :
Facet
Vertex Figure
Dual
Facet Of :
{2,8,2,11,2} of size 1408
Vertex Figure Of :
{2,2,8,2,11} of size 1408
Quotients (Maximal Quotients in Boldface) :
2-fold quotients : {2,4,2,11}*352
4-fold quotients : {2,2,2,11}*176
Covers (Minimal Covers in Boldface) :
2-fold covers : {4,8,2,11}*1408a, {2,16,2,11}*1408, {2,8,2,22}*1408
Permutation Representation (GAP) :
s0 := (1,2);;
s1 := (4,5)(6,7)(8,9);;
s2 := ( 3, 4)( 5, 6)( 7, 8)( 9,10);;
s3 := (12,13)(14,15)(16,17)(18,19)(20,21);;
s4 := (11,12)(13,14)(15,16)(17,18)(19,20);;
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*s1*s0*s1,
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, s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2,
s3*s4*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(21)!(1,2);
s1 := Sym(21)!(4,5)(6,7)(8,9);
s2 := Sym(21)!( 3, 4)( 5, 6)( 7, 8)( 9,10);
s3 := Sym(21)!(12,13)(14,15)(16,17)(18,19)(20,21);
s4 := Sym(21)!(11,12)(13,14)(15,16)(17,18)(19,20);
poly := sub<Sym(21)|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*s1*s0*s1, 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,
s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2,
s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4 >;
to this polytope