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

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {9,2,2,4}*288
if this polytope has a name.
Group : SmallGroup(288,356)
Rank : 5
Schlafli Type : {9,2,2,4}
Number of vertices, edges, etc : 9, 9, 2, 4, 4
Order of s₀s₁s₂s₃s₄ : 36
Order of s₀s₁s₂s₃s₄s₃s₂s₁ : 2
Special Properties :
   Degenerate
   Universal
   Orientable
   Flat
Related Polytopes :
   Facet
   Vertex Figure
   Dual
Facet Of :
   {9,2,2,4,2} of size 576
   {9,2,2,4,3} of size 864
   {9,2,2,4,4} of size 1152
   {9,2,2,4,6} of size 1728
   {9,2,2,4,3} of size 1728
   {9,2,2,4,6} of size 1728
   {9,2,2,4,6} of size 1728
Vertex Figure Of :
   {2,9,2,2,4} of size 576
   {4,9,2,2,4} of size 1152
   {6,9,2,2,4} of size 1728
Quotients (Maximal Quotients in Boldface) :
   2-fold quotients : {9,2,2,2}*144
   3-fold quotients : {3,2,2,4}*96
   6-fold quotients : {3,2,2,2}*48
Covers (Minimal Covers in Boldface) :
   2-fold covers : {9,2,4,4}*576, {9,2,2,8}*576, {18,2,2,4}*576
   3-fold covers : {27,2,2,4}*864, {9,2,2,12}*864, {9,2,6,4}*864a, {9,6,2,4}*864
   4-fold covers : {9,2,4,8}*1152a, {9,2,8,4}*1152a, {9,2,4,8}*1152b, {9,2,8,4}*1152b, {9,2,4,4}*1152, {9,2,2,16}*1152, {18,2,4,4}*1152, {18,4,2,4}*1152a, {36,2,2,4}*1152, {18,2,2,8}*1152, {9,4,2,4}*1152
   5-fold covers : {9,2,2,20}*1440, {9,2,10,4}*1440, {45,2,2,4}*1440
   6-fold covers : {27,2,4,4}*1728, {27,2,2,8}*1728, {54,2,2,4}*1728, {9,2,4,12}*1728a, {9,2,12,4}*1728a, {9,2,2,24}*1728, {9,2,6,8}*1728, {9,6,2,8}*1728, {9,6,4,4}*1728, {18,2,2,12}*1728, {18,2,6,4}*1728a, {18,6,2,4}*1728a, {18,6,2,4}*1728b
Permutation Representation (GAP) :

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

Permutation Representation (Magma) :

s0 := Sym(15)!(2,3)(4,5)(6,7)(8,9);
s1 := Sym(15)!(1,2)(3,4)(5,6)(7,8);
s2 := Sym(15)!(10,11);
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*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*s3*s4*s3*s4, s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1 >;

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