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Polytope of Type {3,10,3}
This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {3,10,3}*1320a
if this polytope has a name.
Group : SmallGroup(1320,134)
Rank : 4
Schlafli Type : {3,10,3}
Number of vertices, edges, etc : 11, 110, 110, 11
Order of s0s1s2s3 : 6
Order of s0s1s2s3s2s1 : 10
Special Properties :
Universal
Non-Orientable
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 : {3,5,3}*660
Covers (Minimal Covers in Boldface) :
None in this atlas.
Permutation Representation (GAP) :
s0 := ( 2, 3)( 5, 9)( 6, 7)( 8,11);;
s1 := ( 3, 4)( 5, 7)( 6,11)( 8, 9);;
s2 := ( 2, 6)( 3, 7)( 4,10)( 8,11)(12,13);;
s3 := ( 1,10)( 5, 7)( 6, 9)( 8,11)(12,13);;
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,
s0*s3*s0*s3, s1*s3*s1*s3, s0*s1*s0*s1*s0*s1,
s2*s3*s2*s3*s2*s3, s0*s1*s2*s1*s2*s0*s1*s2*s1*s2*s0*s1*s2*s1*s2,
s1*s2*s1*s3*s2*s1*s3*s2*s1*s3*s2*s1*s2*s3*s2 ];;
poly := F / rels;;
Permutation Representation (Magma) :
s0 := Sym(13)!( 2, 3)( 5, 9)( 6, 7)( 8,11);
s1 := Sym(13)!( 3, 4)( 5, 7)( 6,11)( 8, 9);
s2 := Sym(13)!( 2, 6)( 3, 7)( 4,10)( 8,11)(12,13);
s3 := Sym(13)!( 1,10)( 5, 7)( 6, 9)( 8,11)(12,13);
poly := sub<Sym(13)|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, s0*s3*s0*s3, s1*s3*s1*s3,
s0*s1*s0*s1*s0*s1, s2*s3*s2*s3*s2*s3,
s0*s1*s2*s1*s2*s0*s1*s2*s1*s2*s0*s1*s2*s1*s2,
s1*s2*s1*s3*s2*s1*s3*s2*s1*s3*s2*s1*s2*s3*s2 >;
References : None.
to this polytope