Polytope of Type {7,2,11,2}
This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {7,2,11,2}*616
if this polytope has a name.
Group : SmallGroup(616,31)
Rank : 5
Schlafli Type : {7,2,11,2}
Number of vertices, edges, etc : 7, 7, 11, 11, 2
Order of s0s1s2s3s4 : 154
Order of s0s1s2s3s4s3s2s1 : 2
Special Properties :
Degenerate
Universal
Orientable
Flat
Related Polytopes :
Facet
Vertex Figure
Dual
Facet Of :
{7,2,11,2,2} of size 1232
{7,2,11,2,3} of size 1848
Vertex Figure Of :
{2,7,2,11,2} of size 1232
Quotients (Maximal Quotients in Boldface) :
No Regular Quotients.
Covers (Minimal Covers in Boldface) :
2-fold covers : {7,2,22,2}*1232, {14,2,11,2}*1232
3-fold covers : {21,2,11,2}*1848, {7,2,33,2}*1848
Permutation Representation (GAP) :
s0 := (2,3)(4,5)(6,7);;
s1 := (1,2)(3,4)(5,6);;
s2 := ( 9,10)(11,12)(13,14)(15,16)(17,18);;
s3 := ( 8, 9)(10,11)(12,13)(14,15)(16,17);;
s4 := (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*s2*s0*s2,
s1*s2*s1*s2, s0*s3*s0*s3, s1*s3*s1*s3,
s0*s4*s0*s4, s1*s4*s1*s4, s2*s4*s2*s4,
s3*s4*s3*s4, s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1,
s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3 ];;
poly := F / rels;;
Permutation Representation (Magma) :
s0 := Sym(20)!(2,3)(4,5)(6,7);
s1 := Sym(20)!(1,2)(3,4)(5,6);
s2 := Sym(20)!( 9,10)(11,12)(13,14)(15,16)(17,18);
s3 := Sym(20)!( 8, 9)(10,11)(12,13)(14,15)(16,17);
s4 := Sym(20)!(19,20);
poly := sub<Sym(20)|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, s1*s2*s1*s2,
s0*s3*s0*s3, s1*s3*s1*s3, s0*s4*s0*s4,
s1*s4*s1*s4, s2*s4*s2*s4, s3*s4*s3*s4,
s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1,
s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3 >;
to this polytope