Polytope of Type {13,2,5}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {13,2,5}*260
if this polytope has a name.
Group : SmallGroup(260,11)
Rank : 4
Schlafli Type : {13,2,5}
Number of vertices, edges, etc : 13, 13, 5, 5
Order of s₀s₁s₂s₃ : 65
Order of s₀s₁s₂s₃s₂s₁ : 2
Special Properties :
   Degenerate
   Universal
   Orientable
   Flat
Related Polytopes :
   Facet
   Vertex Figure
   Dual
Facet Of :
   {13,2,5,2} of size 520
   {13,2,5,3} of size 1560
   {13,2,5,5} of size 1560
Vertex Figure Of :
   {2,13,2,5} of size 520
Quotients (Maximal Quotients in Boldface) :
   No Regular Quotients.
Covers (Minimal Covers in Boldface) :
   2-fold covers : {13,2,10}*520, {26,2,5}*520
   3-fold covers : {13,2,15}*780, {39,2,5}*780
   4-fold covers : {13,2,20}*1040, {52,2,5}*1040, {26,2,10}*1040
   5-fold covers : {13,2,25}*1300, {65,2,5}*1300
   6-fold covers : {13,2,30}*1560, {26,2,15}*1560, {39,2,10}*1560, {78,2,5}*1560
   7-fold covers : {13,2,35}*1820, {91,2,5}*1820
Permutation Representation (GAP) :

s0 := ( 2, 3)( 4, 5)( 6, 7)( 8, 9)(10,11)(12,13);;
s1 := ( 1, 2)( 3, 4)( 5, 6)( 7, 8)( 9,10)(11,12);;
s2 := (15,16)(17,18);;
s3 := (14,15)(16,17);;
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, 
s2*s3*s2*s3*s2*s3*s2*s3*s2*s3, s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1 ];;
poly := F / rels;;

Permutation Representation (Magma) :

s0 := Sym(18)!( 2, 3)( 4, 5)( 6, 7)( 8, 9)(10,11)(12,13);
s1 := Sym(18)!( 1, 2)( 3, 4)( 5, 6)( 7, 8)( 9,10)(11,12);
s2 := Sym(18)!(15,16)(17,18);
s3 := Sym(18)!(14,15)(16,17);
poly := sub<Sym(18)|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, s2*s3*s2*s3*s2*s3*s2*s3*s2*s3, 
s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1 >;

to this polytope