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Polytope of Type {9,2,2,2,3}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {9,2,2,2,3}*432
if this polytope has a name.
Group : SmallGroup(432,544)
Rank : 6
Schlafli Type : {9,2,2,2,3}
Number of vertices, edges, etc : 9, 9, 2, 2, 3, 3
Order of s0s1s2s3s4s5 : 18
Order of s0s1s2s3s4s5s4s3s2s1 : 2
Special Properties :
   Degenerate
   Universal
   Orientable
   Flat
Related Polytopes :
   Facet
   Vertex Figure
   Dual
Facet Of :
   {9,2,2,2,3,2} of size 864
   {9,2,2,2,3,3} of size 1728
   {9,2,2,2,3,4} of size 1728
Vertex Figure Of :
   {2,9,2,2,2,3} of size 864
   {4,9,2,2,2,3} of size 1728
Quotients (Maximal Quotients in Boldface) :
   3-fold quotients : {3,2,2,2,3}*144
Covers (Minimal Covers in Boldface) :
   2-fold covers : {9,2,4,2,3}*864, {9,2,2,2,6}*864, {18,2,2,2,3}*864
   3-fold covers : {9,2,2,2,9}*1296, {27,2,2,2,3}*1296, {9,2,2,6,3}*1296, {9,2,6,2,3}*1296, {9,6,2,2,3}*1296
   4-fold covers : {9,2,8,2,3}*1728, {9,2,2,2,12}*1728, {36,2,2,2,3}*1728, {9,2,2,4,6}*1728a, {9,2,4,2,6}*1728, {18,2,4,2,3}*1728, {18,4,2,2,3}*1728a, {9,2,2,4,3}*1728, {9,4,2,2,3}*1728, {18,2,2,2,6}*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 := (12,13);;
s4 := (15,16);;
s5 := (14,15);;
poly := Group([s0,s1,s2,s3,s4,s5]);;
 
Finitely Presented Group Representation (GAP) :
F := FreeGroup("s0","s1","s2","s3","s4","s5");;
s0 := F.1;;  s1 := F.2;;  s2 := F.3;;  s3 := F.4;;  s4 := F.5;;  s5 := F.6;;  
rels := [ s0*s0, s1*s1, s2*s2, s3*s3, s4*s4, s5*s5, 
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, 
s0*s5*s0*s5, s1*s5*s1*s5, s2*s5*s2*s5, 
s3*s5*s3*s5, s4*s5*s4*s5*s4*s5, 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(16)!(2,3)(4,5)(6,7)(8,9);
s1 := Sym(16)!(1,2)(3,4)(5,6)(7,8);
s2 := Sym(16)!(10,11);
s3 := Sym(16)!(12,13);
s4 := Sym(16)!(15,16);
s5 := Sym(16)!(14,15);
poly := sub<Sym(16)|s0,s1,s2,s3,s4,s5>;
 
Finitely Presented Group Representation (Magma) :
poly<s0,s1,s2,s3,s4,s5> := Group< s0,s1,s2,s3,s4,s5 | s0*s0, s1*s1, s2*s2, 
s3*s3, s4*s4, s5*s5, 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, s0*s5*s0*s5, s1*s5*s1*s5, 
s2*s5*s2*s5, s3*s5*s3*s5, s4*s5*s4*s5*s4*s5, 
s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1 >; 
 

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