Polytope of Type {2,4,6,2}
This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {2,4,6,2}*864
if this polytope has a name.
Group : SmallGroup(864,4007)
Rank : 5
Schlafli Type : {2,4,6,2}
Number of vertices, edges, etc : 2, 18, 54, 27, 2
Order of s0s1s2s3s4 : 12
Order of s0s1s2s3s4s3s2s1 : 2
Special Properties :
Degenerate
Universal
Non-Orientable
Flat
Related Polytopes :
Facet
Vertex Figure
Dual
Facet Of :
{2,4,6,2,2} of size 1728
Vertex Figure Of :
{2,2,4,6,2} of size 1728
Quotients (Maximal Quotients in Boldface) :
3-fold quotients : {2,4,6,2}*288
Covers (Minimal Covers in Boldface) :
2-fold covers : {4,4,6,2}*1728a, {2,4,6,2}*1728a
Permutation Representation (GAP) :
s0 := (1,2);;
s1 := ( 4, 5)( 7, 8)(10,11)(13,14)(15,18)(16,20)(17,19);;
s2 := ( 3,12)( 4,14)( 5,13)( 6,15)( 7,17)( 8,16)( 9,18)(10,20)(11,19);;
s3 := ( 3, 6)( 4, 7)( 5, 8)(15,20)(16,18)(17,19);;
s4 := (21,22);;
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*s1*s0*s1,
s0*s2*s0*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, s1*s2*s1*s2*s1*s2*s1*s2,
s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3,
s2*s3*s2*s1*s2*s3*s1*s2*s1*s2*s3*s2*s1 ];;
poly := F / rels;;
Permutation Representation (Magma) :
s0 := Sym(22)!(1,2);
s1 := Sym(22)!( 4, 5)( 7, 8)(10,11)(13,14)(15,18)(16,20)(17,19);
s2 := Sym(22)!( 3,12)( 4,14)( 5,13)( 6,15)( 7,17)( 8,16)( 9,18)(10,20)(11,19);
s3 := Sym(22)!( 3, 6)( 4, 7)( 5, 8)(15,20)(16,18)(17,19);
s4 := Sym(22)!(21,22);
poly := sub<Sym(22)|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*s1*s0*s1, s0*s2*s0*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,
s1*s2*s1*s2*s1*s2*s1*s2, s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3,
s2*s3*s2*s1*s2*s3*s1*s2*s1*s2*s3*s2*s1 >;
to this polytope