Polytope of Type {2,8,6,2}
This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {2,8,6,2}*384
if this polytope has a name.
Group : SmallGroup(384,19745)
Rank : 5
Schlafli Type : {2,8,6,2}
Number of vertices, edges, etc : 2, 8, 24, 6, 2
Order of s0s1s2s3s4 : 24
Order of s0s1s2s3s4s3s2s1 : 2
Special Properties :
Degenerate
Universal
Orientable
Flat
Related Polytopes :
Facet
Vertex Figure
Dual
Facet Of :
{2,8,6,2,2} of size 768
{2,8,6,2,3} of size 1152
{2,8,6,2,5} of size 1920
Vertex Figure Of :
{2,2,8,6,2} of size 768
{3,2,8,6,2} of size 1152
{5,2,8,6,2} of size 1920
Quotients (Maximal Quotients in Boldface) :
2-fold quotients : {2,4,6,2}*192a
3-fold quotients : {2,8,2,2}*128
4-fold quotients : {2,2,6,2}*96
6-fold quotients : {2,4,2,2}*64
8-fold quotients : {2,2,3,2}*48
12-fold quotients : {2,2,2,2}*32
Covers (Minimal Covers in Boldface) :
2-fold covers : {4,8,6,2}*768a, {2,8,12,2}*768a, {2,8,6,4}*768a, {2,16,6,2}*768
3-fold covers : {2,8,18,2}*1152, {2,8,6,6}*1152a, {2,8,6,6}*1152b, {6,8,6,2}*1152, {2,24,6,2}*1152a, {2,24,6,2}*1152b
5-fold covers : {2,8,30,2}*1920, {2,8,6,10}*1920, {10,8,6,2}*1920, {2,40,6,2}*1920
Permutation Representation (GAP) :
s0 := (1,2);;
s1 := ( 4, 7)( 8,11)( 9,12)(10,13)(14,17)(15,18)(16,19)(20,23)(21,24);;
s2 := ( 3, 4)( 5, 9)( 6, 8)( 7,10)(11,15)(12,14)(13,16)(17,21)(18,20)(19,22)
(23,26)(24,25);;
s3 := ( 3, 5)( 4, 8)( 7,11)(10,14)(13,17)(16,20)(19,23)(22,25);;
s4 := (27,28);;
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,
s0*s4*s0*s4, s1*s4*s1*s4, s2*s4*s2*s4,
s3*s4*s3*s4, s1*s2*s3*s2*s1*s2*s3*s2,
s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3,
s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2 ];;
poly := F / rels;;
Permutation Representation (Magma) :
s0 := Sym(28)!(1,2);
s1 := Sym(28)!( 4, 7)( 8,11)( 9,12)(10,13)(14,17)(15,18)(16,19)(20,23)(21,24);
s2 := Sym(28)!( 3, 4)( 5, 9)( 6, 8)( 7,10)(11,15)(12,14)(13,16)(17,21)(18,20)
(19,22)(23,26)(24,25);
s3 := Sym(28)!( 3, 5)( 4, 8)( 7,11)(10,14)(13,17)(16,20)(19,23)(22,25);
s4 := Sym(28)!(27,28);
poly := sub<Sym(28)|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, s0*s4*s0*s4,
s1*s4*s1*s4, s2*s4*s2*s4, s3*s4*s3*s4,
s1*s2*s3*s2*s1*s2*s3*s2, s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3,
s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2 >;
to this polytope