Polytope of Type {4,6,2}
This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {4,6,2}*432
if this polytope has a name.
Group : SmallGroup(432,530)
Rank : 4
Schlafli Type : {4,6,2}
Number of vertices, edges, etc : 18, 54, 27, 2
Order of s0s1s2s3 : 12
Order of s0s1s2s3s2s1 : 2
Special Properties :
Degenerate
Universal
Non-Orientable
Flat
Related Polytopes :
Facet
Vertex Figure
Dual
Facet Of :
{4,6,2,2} of size 864
{4,6,2,3} of size 1296
{4,6,2,4} of size 1728
Vertex Figure Of :
{2,4,6,2} of size 864
{4,4,6,2} of size 1728
Quotients (Maximal Quotients in Boldface) :
3-fold quotients : {4,6,2}*144
Covers (Minimal Covers in Boldface) :
2-fold covers : {4,6,2}*864a
3-fold covers : {12,6,2}*1296
4-fold covers : {8,6,2}*1728a, {4,6,4}*1728b, {4,12,2}*1728b
Permutation Representation (GAP) :
s0 := ( 2, 3)( 5, 6)( 8, 9)(11,12)(13,16)(14,18)(15,17);;
s1 := ( 1,10)( 2,12)( 3,11)( 4,13)( 5,15)( 6,14)( 7,16)( 8,18)( 9,17);;
s2 := ( 1, 4)( 2, 5)( 3, 6)(13,18)(14,16)(15,17);;
s3 := (19,20);;
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,
s0*s3*s0*s3, s1*s3*s1*s3, s2*s3*s2*s3,
s0*s1*s0*s1*s0*s1*s0*s1, s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2,
s1*s2*s1*s0*s1*s2*s0*s1*s0*s1*s2*s1*s0 ];;
poly := F / rels;;
Permutation Representation (Magma) :
s0 := Sym(20)!( 2, 3)( 5, 6)( 8, 9)(11,12)(13,16)(14,18)(15,17);
s1 := Sym(20)!( 1,10)( 2,12)( 3,11)( 4,13)( 5,15)( 6,14)( 7,16)( 8,18)( 9,17);
s2 := Sym(20)!( 1, 4)( 2, 5)( 3, 6)(13,18)(14,16)(15,17);
s3 := Sym(20)!(19,20);
poly := sub<Sym(20)|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, s0*s3*s0*s3, s1*s3*s1*s3,
s2*s3*s2*s3, s0*s1*s0*s1*s0*s1*s0*s1,
s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2,
s1*s2*s1*s0*s1*s2*s0*s1*s0*s1*s2*s1*s0 >;
to this polytope