Polytope of Type {8,2,13}
This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {8,2,13}*416
if this polytope has a name.
Group : SmallGroup(416,131)
Rank : 4
Schlafli Type : {8,2,13}
Number of vertices, edges, etc : 8, 8, 13, 13
Order of s0s1s2s3 : 104
Order of s0s1s2s3s2s1 : 2
Special Properties :
Degenerate
Universal
Orientable
Flat
Related Polytopes :
Facet
Vertex Figure
Dual
Facet Of :
{8,2,13,2} of size 832
Vertex Figure Of :
{2,8,2,13} of size 832
{4,8,2,13} of size 1664
{4,8,2,13} of size 1664
Quotients (Maximal Quotients in Boldface) :
2-fold quotients : {4,2,13}*208
4-fold quotients : {2,2,13}*104
Covers (Minimal Covers in Boldface) :
2-fold covers : {16,2,13}*832, {8,2,26}*832
3-fold covers : {24,2,13}*1248, {8,2,39}*1248
4-fold covers : {32,2,13}*1664, {8,4,26}*1664a, {8,2,52}*1664, {16,2,26}*1664
Permutation Representation (GAP) :
s0 := (2,3)(4,5)(6,7);;
s1 := (1,2)(3,4)(5,6)(7,8);;
s2 := (10,11)(12,13)(14,15)(16,17)(18,19)(20,21);;
s3 := ( 9,10)(11,12)(13,14)(15,16)(17,18)(19,20);;
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*s2*s0*s2,
s1*s2*s1*s2, s0*s3*s0*s3, s1*s3*s1*s3,
s0*s1*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*s2*s3*s2*s3 ];;
poly := F / rels;;
Permutation Representation (Magma) :
s0 := Sym(21)!(2,3)(4,5)(6,7);
s1 := Sym(21)!(1,2)(3,4)(5,6)(7,8);
s2 := Sym(21)!(10,11)(12,13)(14,15)(16,17)(18,19)(20,21);
s3 := Sym(21)!( 9,10)(11,12)(13,14)(15,16)(17,18)(19,20);
poly := sub<Sym(21)|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*s2*s0*s2, s1*s2*s1*s2, s0*s3*s0*s3,
s1*s3*s1*s3, s0*s1*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*s2*s3*s2*s3 >;
to this polytope