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