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

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

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

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