Polytope of Type {2,9,2,4}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {2,9,2,4}*288
if this polytope has a name.
Group : SmallGroup(288,356)
Rank : 5
Schlafli Type : {2,9,2,4}
Number of vertices, edges, etc : 2, 9, 9, 4, 4
Order of s₀s₁s₂s₃s₄ : 36
Order of s₀s₁s₂s₃s₄s₃s₂s₁ : 2
Special Properties :
   Degenerate
   Universal
   Orientable
   Flat
Related Polytopes :
   Facet
   Vertex Figure
   Dual
Facet Of :
   {2,9,2,4,2} of size 576
   {2,9,2,4,3} of size 864
   {2,9,2,4,4} of size 1152
   {2,9,2,4,6} of size 1728
   {2,9,2,4,3} of size 1728
   {2,9,2,4,6} of size 1728
   {2,9,2,4,6} of size 1728
Vertex Figure Of :
   {2,2,9,2,4} of size 576
   {3,2,9,2,4} of size 864
   {4,2,9,2,4} of size 1152
   {5,2,9,2,4} of size 1440
   {6,2,9,2,4} of size 1728
Quotients (Maximal Quotients in Boldface) :
   2-fold quotients : {2,9,2,2}*144
   3-fold quotients : {2,3,2,4}*96
   6-fold quotients : {2,3,2,2}*48
Covers (Minimal Covers in Boldface) :
   2-fold covers : {2,9,2,8}*576, {2,18,2,4}*576
   3-fold covers : {2,27,2,4}*864, {2,9,2,12}*864, {6,9,2,4}*864, {2,9,6,4}*864
   4-fold covers : {2,9,2,16}*1152, {2,18,4,4}*1152, {4,18,2,4}*1152a, {2,36,2,4}*1152, {2,18,2,8}*1152, {2,9,4,4}*1152b, {4,9,2,4}*1152
   5-fold covers : {2,9,2,20}*1440, {2,45,2,4}*1440
   6-fold covers : {2,27,2,8}*1728, {2,54,2,4}*1728, {2,9,2,24}*1728, {6,9,2,8}*1728, {2,9,6,8}*1728, {2,18,2,12}*1728, {2,18,6,4}*1728a, {6,18,2,4}*1728a, {6,18,2,4}*1728b, {2,18,6,4}*1728b
Permutation Representation (GAP) :

s0 := (1,2);;
s1 := ( 4, 5)( 6, 7)( 8, 9)(10,11);;
s2 := ( 3, 4)( 5, 6)( 7, 8)( 9,10);;
s3 := (13,14);;
s4 := (12,13)(14,15);;
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, s3*s4*s3*s4*s3*s4*s3*s4, 
s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2 ];;
poly := F / rels;;

Permutation Representation (Magma) :

s0 := Sym(15)!(1,2);
s1 := Sym(15)!( 4, 5)( 6, 7)( 8, 9)(10,11);
s2 := Sym(15)!( 3, 4)( 5, 6)( 7, 8)( 9,10);
s3 := Sym(15)!(13,14);
s4 := Sym(15)!(12,13)(14,15);
poly := sub<Sym(15)|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, 
s3*s4*s3*s4*s3*s4*s3*s4, s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2 >;

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