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