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Polytope of Type {9,2,2,6}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {9,2,2,6}*432
if this polytope has a name.
Group : SmallGroup(432,544)
Rank : 5
Schlafli Type : {9,2,2,6}
Number of vertices, edges, etc : 9, 9, 2, 6, 6
Order of s0s1s2s3s4 : 18
Order of s0s1s2s3s4s3s2s1 : 2
Special Properties :
   Degenerate
   Universal
   Orientable
   Flat
Related Polytopes :
   Facet
   Vertex Figure
   Dual
Facet Of :
   {9,2,2,6,2} of size 864
   {9,2,2,6,3} of size 1296
   {9,2,2,6,4} of size 1728
   {9,2,2,6,3} of size 1728
   {9,2,2,6,4} of size 1728
   {9,2,2,6,4} of size 1728
Vertex Figure Of :
   {2,9,2,2,6} of size 864
   {4,9,2,2,6} of size 1728
Quotients (Maximal Quotients in Boldface) :
   2-fold quotients : {9,2,2,3}*216
   3-fold quotients : {9,2,2,2}*144, {3,2,2,6}*144
   6-fold quotients : {3,2,2,3}*72
   9-fold quotients : {3,2,2,2}*48
Covers (Minimal Covers in Boldface) :
   2-fold covers : {9,2,2,12}*864, {9,2,4,6}*864a, {18,2,2,6}*864
   3-fold covers : {9,2,2,18}*1296, {27,2,2,6}*1296, {9,2,6,6}*1296a, {9,2,6,6}*1296b, {9,6,2,6}*1296
   4-fold covers : {9,2,4,12}*1728a, {9,2,2,24}*1728, {9,2,8,6}*1728, {18,2,2,12}*1728, {36,2,2,6}*1728, {18,2,4,6}*1728a, {18,4,2,6}*1728a, {9,2,4,6}*1728, {9,4,2,6}*1728
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 := (14,15)(16,17);;
s4 := (12,16)(13,14)(15,17);;
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*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(17)!(2,3)(4,5)(6,7)(8,9);
s1 := Sym(17)!(1,2)(3,4)(5,6)(7,8);
s2 := Sym(17)!(10,11);
s3 := Sym(17)!(14,15)(16,17);
s4 := Sym(17)!(12,16)(13,14)(15,17);
poly := sub<Sym(17)|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*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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