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Polytope of Type {14,2,5,2}
This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {14,2,5,2}*560
if this polytope has a name.
Group : SmallGroup(560,176)
Rank : 5
Schlafli Type : {14,2,5,2}
Number of vertices, edges, etc : 14, 14, 5, 5, 2
Order of s0s1s2s3s4 : 70
Order of s0s1s2s3s4s3s2s1 : 2
Special Properties :
Degenerate
Universal
Orientable
Flat
Related Polytopes :
Facet
Vertex Figure
Dual
Facet Of :
{14,2,5,2,2} of size 1120
{14,2,5,2,3} of size 1680
Vertex Figure Of :
{2,14,2,5,2} of size 1120
Quotients (Maximal Quotients in Boldface) :
2-fold quotients : {7,2,5,2}*280
7-fold quotients : {2,2,5,2}*80
Covers (Minimal Covers in Boldface) :
2-fold covers : {28,2,5,2}*1120, {14,2,10,2}*1120
3-fold covers : {14,2,15,2}*1680, {42,2,5,2}*1680
Permutation Representation (GAP) :
s0 := ( 3, 4)( 5, 6)( 7, 8)( 9,10)(11,12)(13,14);;
s1 := ( 1, 5)( 2, 3)( 4, 9)( 6, 7)( 8,13)(10,11)(12,14);;
s2 := (16,17)(18,19);;
s3 := (15,16)(17,18);;
s4 := (20,21);;
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,
s3*s4*s3*s4, s2*s3*s2*s3*s2*s3*s2*s3*s2*s3,
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*s0*s1 ];;
poly := F / rels;;
Permutation Representation (Magma) :
s0 := Sym(21)!( 3, 4)( 5, 6)( 7, 8)( 9,10)(11,12)(13,14);
s1 := Sym(21)!( 1, 5)( 2, 3)( 4, 9)( 6, 7)( 8,13)(10,11)(12,14);
s2 := Sym(21)!(16,17)(18,19);
s3 := Sym(21)!(15,16)(17,18);
s4 := Sym(21)!(20,21);
poly := sub<Sym(21)|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, s3*s4*s3*s4,
s2*s3*s2*s3*s2*s3*s2*s3*s2*s3, 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*s0*s1 >;
to this polytope