Polytope of Type {2,2,9,2,2}
This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {2,2,9,2,2}*288
if this polytope has a name.
Group : SmallGroup(288,839)
Rank : 6
Schlafli Type : {2,2,9,2,2}
Number of vertices, edges, etc : 2, 2, 9, 9, 2, 2
Order of s0s1s2s3s4s5 : 18
Order of s0s1s2s3s4s5s4s3s2s1 : 2
Special Properties :
Degenerate
Universal
Orientable
Flat
Self-Dual
Related Polytopes :
Facet
Vertex Figure
Dual
Facet Of :
{2,2,9,2,2,2} of size 576
{2,2,9,2,2,3} of size 864
{2,2,9,2,2,4} of size 1152
{2,2,9,2,2,5} of size 1440
{2,2,9,2,2,6} of size 1728
Vertex Figure Of :
{2,2,2,9,2,2} of size 576
{3,2,2,9,2,2} of size 864
{4,2,2,9,2,2} of size 1152
{5,2,2,9,2,2} of size 1440
{6,2,2,9,2,2} of size 1728
Quotients (Maximal Quotients in Boldface) :
3-fold quotients : {2,2,3,2,2}*96
Covers (Minimal Covers in Boldface) :
2-fold covers : {2,2,9,2,4}*576, {4,2,9,2,2}*576, {2,2,18,2,2}*576
3-fold covers : {2,2,27,2,2}*864, {2,2,9,2,6}*864, {2,2,9,6,2}*864, {2,6,9,2,2}*864, {6,2,9,2,2}*864
4-fold covers : {4,2,9,2,4}*1152, {2,2,9,2,8}*1152, {8,2,9,2,2}*1152, {2,2,18,2,4}*1152, {2,2,18,4,2}*1152a, {2,4,18,2,2}*1152a, {4,2,18,2,2}*1152, {2,2,36,2,2}*1152, {2,2,9,4,2}*1152, {2,4,9,2,2}*1152
5-fold covers : {2,2,9,2,10}*1440, {10,2,9,2,2}*1440, {2,2,45,2,2}*1440
6-fold covers : {2,2,27,2,4}*1728, {4,2,27,2,2}*1728, {2,2,54,2,2}*1728, {2,2,9,2,12}*1728, {12,2,9,2,2}*1728, {2,6,9,2,4}*1728, {4,2,9,2,6}*1728, {4,2,9,6,2}*1728, {6,2,9,2,4}*1728, {2,2,9,6,4}*1728, {4,6,9,2,2}*1728, {2,2,18,2,6}*1728, {2,2,18,6,2}*1728a, {2,2,18,6,2}*1728b, {2,6,18,2,2}*1728a, {2,6,18,2,2}*1728b, {6,2,18,2,2}*1728
Permutation Representation (GAP) :
s0 := (1,2);;
s1 := (3,4);;
s2 := ( 6, 7)( 8, 9)(10,11)(12,13);;
s3 := ( 5, 6)( 7, 8)( 9,10)(11,12);;
s4 := (14,15);;
s5 := (16,17);;
poly := Group([s0,s1,s2,s3,s4,s5]);;
Finitely Presented Group Representation (GAP) :
F := FreeGroup("s0","s1","s2","s3","s4","s5");;
s0 := F.1;; s1 := F.2;; s2 := F.3;; s3 := F.4;; s4 := F.5;; s5 := F.6;;
rels := [ s0*s0, s1*s1, s2*s2, s3*s3, s4*s4, s5*s5,
s0*s1*s0*s1, s0*s2*s0*s2, s1*s2*s1*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,
s0*s5*s0*s5, s1*s5*s1*s5, s2*s5*s2*s5,
s3*s5*s3*s5, s4*s5*s4*s5, s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3 ];;
poly := F / rels;;
Permutation Representation (Magma) :
s0 := Sym(17)!(1,2);
s1 := Sym(17)!(3,4);
s2 := Sym(17)!( 6, 7)( 8, 9)(10,11)(12,13);
s3 := Sym(17)!( 5, 6)( 7, 8)( 9,10)(11,12);
s4 := Sym(17)!(14,15);
s5 := Sym(17)!(16,17);
poly := sub<Sym(17)|s0,s1,s2,s3,s4,s5>;
Finitely Presented Group Representation (Magma) :
poly<s0,s1,s2,s3,s4,s5> := Group< s0,s1,s2,s3,s4,s5 | s0*s0, s1*s1, s2*s2,
s3*s3, s4*s4, s5*s5, s0*s1*s0*s1, s0*s2*s0*s2,
s1*s2*s1*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, s0*s5*s0*s5, s1*s5*s1*s5,
s2*s5*s2*s5, s3*s5*s3*s5, s4*s5*s4*s5,
s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3 >;
to this polytope