Polytope of Type {5,2,13}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {5,2,13}*260
if this polytope has a name.
Group : SmallGroup(260,11)
Rank : 4
Schlafli Type : {5,2,13}
Number of vertices, edges, etc : 5, 5, 13, 13
Order of s₀s₁s₂s₃ : 65
Order of s₀s₁s₂s₃s₂s₁ : 2
Special Properties :
   Degenerate
   Universal
   Orientable
   Flat
Related Polytopes :
   Facet
   Vertex Figure
   Dual
Facet Of :
   {5,2,13,2} of size 520
Vertex Figure Of :
   {2,5,2,13} of size 520
   {3,5,2,13} of size 1560
   {5,5,2,13} of size 1560
Quotients (Maximal Quotients in Boldface) :
   No Regular Quotients.
Covers (Minimal Covers in Boldface) :
   2-fold covers : {5,2,26}*520, {10,2,13}*520
   3-fold covers : {15,2,13}*780, {5,2,39}*780
   4-fold covers : {20,2,13}*1040, {5,2,52}*1040, {10,2,26}*1040
   5-fold covers : {25,2,13}*1300, {5,2,65}*1300
   6-fold covers : {15,2,26}*1560, {30,2,13}*1560, {5,2,78}*1560, {10,2,39}*1560
   7-fold covers : {35,2,13}*1820, {5,2,91}*1820
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);;
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, 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(18)!(2,3)(4,5);
s1 := Sym(18)!(1,2)(3,4);
s2 := Sym(18)!( 7, 8)( 9,10)(11,12)(13,14)(15,16)(17,18);
s3 := Sym(18)!( 6, 7)( 8, 9)(10,11)(12,13)(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, 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 >;

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