Polytope of Type {5,2,13,2}
This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {5,2,13,2}*520
if this polytope has a name.
Group : SmallGroup(520,45)
Rank : 5
Schlafli Type : {5,2,13,2}
Number of vertices, edges, etc : 5, 5, 13, 13, 2
Order of s0s1s2s3s4 : 130
Order of s0s1s2s3s4s3s2s1 : 2
Special Properties :
Degenerate
Universal
Orientable
Flat
Related Polytopes :
Facet
Vertex Figure
Dual
Facet Of :
{5,2,13,2,2} of size 1040
{5,2,13,2,3} of size 1560
Vertex Figure Of :
{2,5,2,13,2} of size 1040
Quotients (Maximal Quotients in Boldface) :
No Regular Quotients.
Covers (Minimal Covers in Boldface) :
2-fold covers : {5,2,26,2}*1040, {10,2,13,2}*1040
3-fold covers : {15,2,13,2}*1560, {5,2,39,2}*1560
Permutation Representation (GAP) :
s0 := (2,3)(4,5);;
s1 := (1,2)(3,4);;
s2 := ( 7, 8)( 9,10)(11,12)(13,14)(15,16)(17,18);;
s3 := ( 6, 7)( 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,
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(20)!(2,3)(4,5);
s1 := Sym(20)!(1,2)(3,4);
s2 := Sym(20)!( 7, 8)( 9,10)(11,12)(13,14)(15,16)(17,18);
s3 := Sym(20)!( 6, 7)( 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, 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