Polytope of Type {3,12}
This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {3,12}*576
if this polytope has a name.
Group : SmallGroup(576,8653)
Rank : 3
Schlafli Type : {3,12}
Number of vertices, edges, etc : 24, 144, 96
Order of s0s1s2 : 12
Order of s0s1s2s1 : 12
Special Properties :
Compact Hyperbolic Quotient
Locally Spherical
Orientable
Related Polytopes :
Facet
Vertex Figure
Dual
Petrial
Facet Of :
{3,12,2} of size 1152
Vertex Figure Of :
{2,3,12} of size 1152
Quotients (Maximal Quotients in Boldface) :
4-fold quotients : {3,6}*144, {3,12}*144
12-fold quotients : {3,4}*48, {3,6}*48
16-fold quotients : {3,6}*36
24-fold quotients : {3,3}*24, {3,4}*24
48-fold quotients : {3,2}*12
Covers (Minimal Covers in Boldface) :
2-fold covers : {3,12}*1152b, {3,24}*1152b, {6,12}*1152g, {3,24}*1152c, {6,12}*1152j
3-fold covers : {9,12}*1728, {3,12}*1728
Permutation Representation (GAP) :
s0 := ( 2, 3)( 5, 9)( 6,11)( 7,10)( 8,12)(14,15);;
s1 := ( 2, 4)( 5,13)( 6,16)( 7,15)( 8,14)(10,12);;
s2 := ( 1,16)( 2,14)( 3,15)( 4,13)( 5,12)( 6,10)( 7,11)( 8, 9);;
poly := Group([s0,s1,s2]);;
Finitely Presented Group Representation (GAP) :
F := FreeGroup("s0","s1","s2");;
s0 := F.1;; s1 := F.2;; s2 := F.3;;
rels := [ s0*s0, s1*s1, s2*s2, s0*s2*s0*s2, s0*s1*s0*s1*s0*s1,
s2*s0*s1*s2*s1*s2*s0*s1*s2*s1*s2*s0*s1*s2*s1*s2*s0*s1*s2*s1,
s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2 ];;
poly := F / rels;;
Permutation Representation (Magma) :
s0 := Sym(16)!( 2, 3)( 5, 9)( 6,11)( 7,10)( 8,12)(14,15);
s1 := Sym(16)!( 2, 4)( 5,13)( 6,16)( 7,15)( 8,14)(10,12);
s2 := Sym(16)!( 1,16)( 2,14)( 3,15)( 4,13)( 5,12)( 6,10)( 7,11)( 8, 9);
poly := sub<Sym(16)|s0,s1,s2>;
Finitely Presented Group Representation (Magma) :
poly<s0,s1,s2> := Group< s0,s1,s2 | s0*s0, s1*s1, s2*s2,
s0*s2*s0*s2, s0*s1*s0*s1*s0*s1, s2*s0*s1*s2*s1*s2*s0*s1*s2*s1*s2*s0*s1*s2*s1*s2*s0*s1*s2*s1,
s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2 >;
References : None.
to this polytope