Polytope of Type {2,8,2,12}
This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {2,8,2,12}*768
if this polytope has a name.
Group : SmallGroup(768,1044762)
Rank : 5
Schlafli Type : {2,8,2,12}
Number of vertices, edges, etc : 2, 8, 8, 12, 12
Order of s0s1s2s3s4 : 24
Order of s0s1s2s3s4s3s2s1 : 2
Special Properties :
Degenerate
Universal
Orientable
Flat
Related Polytopes :
Facet
Vertex Figure
Dual
Facet Of :
None in this Atlas
Vertex Figure Of :
None in this Atlas
Quotients (Maximal Quotients in Boldface) :
2-fold quotients : {2,4,2,12}*384, {2,8,2,6}*384
3-fold quotients : {2,8,2,4}*256
4-fold quotients : {2,8,2,3}*192, {2,2,2,12}*192, {2,4,2,6}*192
6-fold quotients : {2,4,2,4}*128, {2,8,2,2}*128
8-fold quotients : {2,4,2,3}*96, {2,2,2,6}*96
12-fold quotients : {2,2,2,4}*64, {2,4,2,2}*64
16-fold quotients : {2,2,2,3}*48
24-fold quotients : {2,2,2,2}*32
Covers (Minimal Covers in Boldface) :
None in this atlas.
Permutation Representation (GAP) :
s0 := (1,2);;
s1 := (4,5)(6,7)(8,9);;
s2 := ( 3, 4)( 5, 6)( 7, 8)( 9,10);;
s3 := (12,13)(14,15)(17,20)(18,19)(21,22);;
s4 := (11,17)(12,14)(13,21)(15,18)(16,19)(20,22);;
poly := Group([s0,s1,s2,s3,s4]);;
Finitely Presented Group Representation (GAP) :
F := FreeGroup("s0","s1","s2","s3","s4");;
s0 := F.1;; s1 := F.2;; s2 := F.3;; s3 := F.4;; s4 := F.5;;
rels := [ s0*s0, s1*s1, s2*s2, s3*s3, s4*s4, s0*s1*s0*s1,
s0*s2*s0*s2, s0*s3*s0*s3, s1*s3*s1*s3,
s2*s3*s2*s3, s0*s4*s0*s4, s1*s4*s1*s4,
s2*s4*s2*s4, s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2,
s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4 ];;
poly := F / rels;;
Permutation Representation (Magma) :
s0 := Sym(22)!(1,2);
s1 := Sym(22)!(4,5)(6,7)(8,9);
s2 := Sym(22)!( 3, 4)( 5, 6)( 7, 8)( 9,10);
s3 := Sym(22)!(12,13)(14,15)(17,20)(18,19)(21,22);
s4 := Sym(22)!(11,17)(12,14)(13,21)(15,18)(16,19)(20,22);
poly := sub<Sym(22)|s0,s1,s2,s3,s4>;
Finitely Presented Group Representation (Magma) :
poly<s0,s1,s2,s3,s4> := Group< s0,s1,s2,s3,s4 | s0*s0, s1*s1, s2*s2,
s3*s3, s4*s4, s0*s1*s0*s1, s0*s2*s0*s2,
s0*s3*s0*s3, s1*s3*s1*s3, s2*s3*s2*s3,
s0*s4*s0*s4, s1*s4*s1*s4, s2*s4*s2*s4,
s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2,
s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4 >;
to this polytope