Polytope of Type {2,2,5,2,5,2,2}
This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {2,2,5,2,5,2,2}*1600
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Group : SmallGroup(1600,10278)
Rank : 8
Schlafli Type : {2,2,5,2,5,2,2}
Number of vertices, edges, etc : 2, 2, 5, 5, 5, 5, 2, 2
Order of s0s1s2s3s4s5s6s7 : 10
Order of s0s1s2s3s4s5s6s7s6s5s4s3s2s1 : 2
Special Properties :
Degenerate
Universal
Orientable
Flat
Self-Dual
Related Polytopes :
Facet
Vertex Figure
Dual
Facet Of :
None in this Atlas
Vertex Figure Of :
None in this Atlas
Quotients (Maximal Quotients in Boldface) :
No Regular Quotients.
Covers (Minimal Covers in Boldface) :
None in this atlas.
Permutation Representation (GAP) :
s0 := (1,2);;
s1 := (3,4);;
s2 := (6,7)(8,9);;
s3 := (5,6)(7,8);;
s4 := (11,12)(13,14);;
s5 := (10,11)(12,13);;
s6 := (15,16);;
s7 := (17,18);;
poly := Group([s0,s1,s2,s3,s4,s5,s6,s7]);;
Finitely Presented Group Representation (GAP) :
F := FreeGroup("s0","s1","s2","s3","s4","s5","s6","s7");;
s0 := F.1;; s1 := F.2;; s2 := F.3;; s3 := F.4;; s4 := F.5;; s5 := F.6;; s6 := F.7;; s7 := F.8;;
rels := [ s0*s0, s1*s1, s2*s2, s3*s3, s4*s4, s5*s5,
s6*s6, s7*s7, s0*s1*s0*s1, 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*s5*s0*s5, s1*s5*s1*s5,
s2*s5*s2*s5, s3*s5*s3*s5, s0*s6*s0*s6,
s1*s6*s1*s6, s2*s6*s2*s6, s3*s6*s3*s6,
s4*s6*s4*s6, s5*s6*s5*s6, s0*s7*s0*s7,
s1*s7*s1*s7, s2*s7*s2*s7, s3*s7*s3*s7,
s4*s7*s4*s7, s5*s7*s5*s7, s6*s7*s6*s7,
s2*s3*s2*s3*s2*s3*s2*s3*s2*s3, s4*s5*s4*s5*s4*s5*s4*s5*s4*s5 ];;
poly := F / rels;;
Permutation Representation (Magma) :
s0 := Sym(18)!(1,2);
s1 := Sym(18)!(3,4);
s2 := Sym(18)!(6,7)(8,9);
s3 := Sym(18)!(5,6)(7,8);
s4 := Sym(18)!(11,12)(13,14);
s5 := Sym(18)!(10,11)(12,13);
s6 := Sym(18)!(15,16);
s7 := Sym(18)!(17,18);
poly := sub<Sym(18)|s0,s1,s2,s3,s4,s5,s6,s7>;
Finitely Presented Group Representation (Magma) :
poly<s0,s1,s2,s3,s4,s5,s6,s7> := Group< s0,s1,s2,s3,s4,s5,s6,s7 | s0*s0, s1*s1, s2*s2,
s3*s3, s4*s4, s5*s5, s6*s6, s7*s7, s0*s1*s0*s1,
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*s5*s0*s5,
s1*s5*s1*s5, s2*s5*s2*s5, s3*s5*s3*s5,
s0*s6*s0*s6, s1*s6*s1*s6, s2*s6*s2*s6,
s3*s6*s3*s6, s4*s6*s4*s6, s5*s6*s5*s6,
s0*s7*s0*s7, s1*s7*s1*s7, s2*s7*s2*s7,
s3*s7*s3*s7, s4*s7*s4*s7, s5*s7*s5*s7,
s6*s7*s6*s7, s2*s3*s2*s3*s2*s3*s2*s3*s2*s3,
s4*s5*s4*s5*s4*s5*s4*s5*s4*s5 >;
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