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Polytope of Type {13,2,6,6}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {13,2,6,6}*1872b
if this polytope has a name.
Group : SmallGroup(1872,1061)
Rank : 5
Schlafli Type : {13,2,6,6}
Number of vertices, edges, etc : 13, 13, 6, 18, 6
Order of s0s1s2s3s4 : 78
Order of s0s1s2s3s4s3s2s1 : 2
Special Properties :
Degenerate
Universal
Orientable
Flat
Related Polytopes :
Facet
Vertex Figure
Dual
Facet Of :
None in this Atlas
Vertex Figure Of :
None in this Atlas
Quotients (Maximal Quotients in Boldface) :
2-fold quotients : {13,2,6,3}*936
3-fold quotients : {13,2,2,6}*624
6-fold quotients : {13,2,2,3}*312
9-fold quotients : {13,2,2,2}*208
Covers (Minimal Covers in Boldface) :
None in this atlas.
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 := (18,19)(22,23)(24,25)(26,27)(28,29)(30,31);;
s3 := (14,18)(15,22)(16,26)(17,24)(20,30)(21,28)(25,27)(29,31);;
s4 := (14,20)(15,16)(17,21)(18,29)(19,28)(22,25)(23,24)(26,31)(27,30);;
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,
s4*s2*s3*s2*s3*s4*s2*s3*s2*s3, s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3,
s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4,
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(31)!( 2, 3)( 4, 5)( 6, 7)( 8, 9)(10,11)(12,13);
s1 := Sym(31)!( 1, 2)( 3, 4)( 5, 6)( 7, 8)( 9,10)(11,12);
s2 := Sym(31)!(18,19)(22,23)(24,25)(26,27)(28,29)(30,31);
s3 := Sym(31)!(14,18)(15,22)(16,26)(17,24)(20,30)(21,28)(25,27)(29,31);
s4 := Sym(31)!(14,20)(15,16)(17,21)(18,29)(19,28)(22,25)(23,24)(26,31)(27,30);
poly := sub<Sym(31)|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, s4*s2*s3*s2*s3*s4*s2*s3*s2*s3,
s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3,
s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4,
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