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Polytope of Type {2,9,2,5}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {2,9,2,5}*360
if this polytope has a name.
Group : SmallGroup(360,45)
Rank : 5
Schlafli Type : {2,9,2,5}
Number of vertices, edges, etc : 2, 9, 9, 5, 5
Order of s0s1s2s3s4 : 90
Order of s0s1s2s3s4s3s2s1 : 2
Special Properties :
   Degenerate
   Universal
   Orientable
   Flat
Related Polytopes :
   Facet
   Vertex Figure
   Dual
Facet Of :
   {2,9,2,5,2} of size 720
Vertex Figure Of :
   {2,2,9,2,5} of size 720
   {3,2,9,2,5} of size 1080
   {4,2,9,2,5} of size 1440
   {5,2,9,2,5} of size 1800
Quotients (Maximal Quotients in Boldface) :
   3-fold quotients : {2,3,2,5}*120
Covers (Minimal Covers in Boldface) :
   2-fold covers : {2,9,2,10}*720, {2,18,2,5}*720
   3-fold covers : {2,27,2,5}*1080, {6,9,2,5}*1080, {2,9,2,15}*1080
   4-fold covers : {2,36,2,5}*1440, {2,9,2,20}*1440, {4,18,2,5}*1440a, {4,9,2,5}*1440, {2,18,2,10}*1440
   5-fold covers : {2,9,2,25}*1800, {2,45,2,5}*1800
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)(15,16);;
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*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(16)!(1,2);
s1 := Sym(16)!( 4, 5)( 6, 7)( 8, 9)(10,11);
s2 := Sym(16)!( 3, 4)( 5, 6)( 7, 8)( 9,10);
s3 := Sym(16)!(13,14)(15,16);
s4 := Sym(16)!(12,13)(14,15);
poly := sub<Sym(16)|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*s3*s4, s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2 >; 
 

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