Polytope of Type {2,6,12}
This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {2,6,12}*864h
if this polytope has a name.
Group : SmallGroup(864,4686)
Rank : 4
Schlafli Type : {2,6,12}
Number of vertices, edges, etc : 2, 18, 108, 36
Order of s0s1s2s3 : 4
Order of s0s1s2s3s2s1 : 2
Special Properties :
Degenerate
Universal
Orientable
Flat
Related Polytopes :
Facet
Vertex Figure
Dual
Facet Of :
{2,6,12,2} of size 1728
Vertex Figure Of :
{2,2,6,12} of size 1728
Quotients (Maximal Quotients in Boldface) :
3-fold quotients : {2,6,4}*288
6-fold quotients : {2,6,4}*144
27-fold quotients : {2,2,4}*32
54-fold quotients : {2,2,2}*16
Covers (Minimal Covers in Boldface) :
2-fold covers : {2,12,12}*1728j, {2,6,24}*1728g, {4,6,12}*1728m
Permutation Representation (GAP) :
s0 := (1,2);;
s1 := ( 4, 5)( 6, 9)( 7,11)( 8,10)(13,14)(15,18)(16,20)(17,19);;
s2 := ( 3,16)( 4,15)( 5,17)( 6,19)( 7,18)( 8,20)( 9,13)(10,12)(11,14);;
s3 := ( 4, 5)( 6, 9)( 7,11)( 8,10)(13,14)(16,17)(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*s1*s0*s1,
s0*s2*s0*s2, s0*s3*s0*s3, s1*s3*s1*s3,
s3*s1*s2*s3*s1*s2*s3*s1*s2*s3*s1*s2,
s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2,
s3*s1*s2*s1*s2*s3*s2*s1*s2*s3*s1*s2*s1*s2*s3*s2*s1*s2 ];;
poly := F / rels;;
Permutation Representation (Magma) :
s0 := Sym(20)!(1,2);
s1 := Sym(20)!( 4, 5)( 6, 9)( 7,11)( 8,10)(13,14)(15,18)(16,20)(17,19);
s2 := Sym(20)!( 3,16)( 4,15)( 5,17)( 6,19)( 7,18)( 8,20)( 9,13)(10,12)(11,14);
s3 := Sym(20)!( 4, 5)( 6, 9)( 7,11)( 8,10)(13,14)(16,17)(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*s1*s0*s1, s0*s2*s0*s2, s0*s3*s0*s3,
s1*s3*s1*s3, s3*s1*s2*s3*s1*s2*s3*s1*s2*s3*s1*s2,
s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2,
s3*s1*s2*s1*s2*s3*s2*s1*s2*s3*s1*s2*s1*s2*s3*s2*s1*s2 >;
to this polytope