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