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Polytope of Type {7,2,6,6}
This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {7,2,6,6}*1008c
if this polytope has a name.
Group : SmallGroup(1008,922)
Rank : 5
Schlafli Type : {7,2,6,6}
Number of vertices, edges, etc : 7, 7, 6, 18, 6
Order of s0s1s2s3s4 : 42
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 : {7,2,3,6}*504
3-fold quotients : {7,2,6,2}*336
6-fold quotients : {7,2,3,2}*168
9-fold quotients : {7,2,2,2}*112
Covers (Minimal Covers in Boldface) :
None in this atlas.
Permutation Representation (GAP) :
s0 := (2,3)(4,5)(6,7);;
s1 := (1,2)(3,4)(5,6);;
s2 := (10,11)(12,13)(14,15)(16,17)(18,21)(19,20)(22,25)(23,24);;
s3 := ( 8,22)( 9,18)(10,16)(11,24)(12,14)(13,23)(15,20)(17,19)(21,25);;
s4 := (12,13)(16,17)(18,19)(20,21)(22,23)(24,25);;
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*s4*s3*s4*s2*s3*s4*s3, s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3,
s2*s3*s4*s3*s2*s3*s2*s3*s4*s3*s2*s3,
s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1 ];;
poly := F / rels;;
Permutation Representation (Magma) :
s0 := Sym(25)!(2,3)(4,5)(6,7);
s1 := Sym(25)!(1,2)(3,4)(5,6);
s2 := Sym(25)!(10,11)(12,13)(14,15)(16,17)(18,21)(19,20)(22,25)(23,24);
s3 := Sym(25)!( 8,22)( 9,18)(10,16)(11,24)(12,14)(13,23)(15,20)(17,19)(21,25);
s4 := Sym(25)!(12,13)(16,17)(18,19)(20,21)(22,23)(24,25);
poly := sub<Sym(25)|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*s4*s3*s4*s2*s3*s4*s3,
s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3,
s2*s3*s4*s3*s2*s3*s2*s3*s4*s3*s2*s3,
s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1 >;
to this polytope