Polytope of Type {7,2,15}
This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {7,2,15}*420
if this polytope has a name.
Group : SmallGroup(420,26)
Rank : 4
Schlafli Type : {7,2,15}
Number of vertices, edges, etc : 7, 7, 15, 15
Order of s0s1s2s3 : 105
Order of s0s1s2s3s2s1 : 2
Special Properties :
Degenerate
Universal
Orientable
Flat
Related Polytopes :
Facet
Vertex Figure
Dual
Facet Of :
{7,2,15,2} of size 840
{7,2,15,4} of size 1680
Vertex Figure Of :
{2,7,2,15} of size 840
Quotients (Maximal Quotients in Boldface) :
3-fold quotients : {7,2,5}*140
5-fold quotients : {7,2,3}*84
Covers (Minimal Covers in Boldface) :
2-fold covers : {7,2,30}*840, {14,2,15}*840
3-fold covers : {7,2,45}*1260, {21,2,15}*1260
4-fold covers : {7,2,60}*1680, {28,2,15}*1680, {14,2,30}*1680
Permutation Representation (GAP) :
s0 := (2,3)(4,5)(6,7);;
s1 := (1,2)(3,4)(5,6);;
s2 := ( 9,10)(11,12)(13,14)(15,16)(17,18)(19,20)(21,22);;
s3 := ( 8, 9)(10,11)(12,13)(14,15)(16,17)(18,19)(20,21);;
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,
s1*s2*s1*s2, s0*s3*s0*s3, s1*s3*s1*s3,
s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1,
s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3 ];;
poly := F / rels;;
Permutation Representation (Magma) :
s0 := Sym(22)!(2,3)(4,5)(6,7);
s1 := Sym(22)!(1,2)(3,4)(5,6);
s2 := Sym(22)!( 9,10)(11,12)(13,14)(15,16)(17,18)(19,20)(21,22);
s3 := Sym(22)!( 8, 9)(10,11)(12,13)(14,15)(16,17)(18,19)(20,21);
poly := sub<Sym(22)|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, s1*s2*s1*s2, s0*s3*s0*s3,
s1*s3*s1*s3, s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1,
s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3 >;
to this polytope