Polytope of Type {8,2,9}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {8,2,9}*288
if this polytope has a name.
Group : SmallGroup(288,120)
Rank : 4
Schlafli Type : {8,2,9}
Number of vertices, edges, etc : 8, 8, 9, 9
Order of s₀s₁s₂s₃ : 72
Order of s₀s₁s₂s₃s₂s₁ : 2
Special Properties :
   Degenerate
   Universal
   Orientable
   Flat
Related Polytopes :
   Facet
   Vertex Figure
   Dual
Facet Of :
   {8,2,9,2} of size 576
   {8,2,9,4} of size 1152
   {8,2,9,6} of size 1728
Vertex Figure Of :
   {2,8,2,9} of size 576
   {4,8,2,9} of size 1152
   {4,8,2,9} of size 1152
   {6,8,2,9} of size 1728
   {3,8,2,9} of size 1728
Quotients (Maximal Quotients in Boldface) :
   2-fold quotients : {4,2,9}*144
   3-fold quotients : {8,2,3}*96
   4-fold quotients : {2,2,9}*72
   6-fold quotients : {4,2,3}*48
   12-fold quotients : {2,2,3}*24
Covers (Minimal Covers in Boldface) :
   2-fold covers : {16,2,9}*576, {8,2,18}*576
   3-fold covers : {8,2,27}*864, {24,2,9}*864, {8,6,9}*864
   4-fold covers : {32,2,9}*1152, {8,4,18}*1152a, {8,2,36}*1152, {16,2,18}*1152, {8,4,9}*1152
   5-fold covers : {40,2,9}*1440, {8,2,45}*1440
   6-fold covers : {16,2,27}*1728, {8,2,54}*1728, {48,2,9}*1728, {16,6,9}*1728, {24,2,18}*1728, {8,6,18}*1728a, {8,6,18}*1728b
Permutation Representation (GAP) :

s0 := (2,3)(4,5)(6,7);;
s1 := (1,2)(3,4)(5,6)(7,8);;
s2 := (10,11)(12,13)(14,15)(16,17);;
s3 := ( 9,10)(11,12)(13,14)(15,16);;
poly := Group([s0,s1,s2,s3]);;

Finitely Presented Group Representation (GAP) :

F := FreeGroup("s0","s1","s2","s3");;
s0 := F.1;;  s1 := F.2;;  s2 := F.3;;  s3 := F.4;;  
rels := [ s0*s0, s1*s1, s2*s2, s3*s3, s0*s2*s0*s2, 
s1*s2*s1*s2, s0*s3*s0*s3, s1*s3*s1*s3, 
s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1, 
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)!(2,3)(4,5)(6,7);
s1 := Sym(17)!(1,2)(3,4)(5,6)(7,8);
s2 := Sym(17)!(10,11)(12,13)(14,15)(16,17);
s3 := Sym(17)!( 9,10)(11,12)(13,14)(15,16);
poly := sub<Sym(17)|s0,s1,s2,s3>;

Finitely Presented Group Representation (Magma) :

poly<s0,s1,s2,s3> := Group< s0,s1,s2,s3 | s0*s0, s1*s1, s2*s2, 
s3*s3, s0*s2*s0*s2, s1*s2*s1*s2, s0*s3*s0*s3, 
s1*s3*s1*s3, s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1, 
s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3 >;

to this polytope