Questions?
See the FAQ
or other info.

Polytope of Type {3,4,2,9}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {3,4,2,9}*432
if this polytope has a name.
Group : SmallGroup(432,521)
Rank : 5
Schlafli Type : {3,4,2,9}
Number of vertices, edges, etc : 3, 6, 4, 9, 9
Order of s0s1s2s3s4 : 9
Order of s0s1s2s3s4s3s2s1 : 2
Special Properties :
   Degenerate
   Universal
   Non-Orientable
   Flat
Related Polytopes :
   Facet
   Vertex Figure
   Dual
Facet Of :
   {3,4,2,9,2} of size 864
   {3,4,2,9,4} of size 1728
Vertex Figure Of :
   {2,3,4,2,9} of size 864
   {4,3,4,2,9} of size 1728
Quotients (Maximal Quotients in Boldface) :
   3-fold quotients : {3,4,2,3}*144
Covers (Minimal Covers in Boldface) :
   2-fold covers : {3,4,2,9}*864, {3,4,2,18}*864, {6,4,2,9}*864b, {6,4,2,9}*864c
   3-fold covers : {3,4,2,27}*1296, {9,4,2,9}*1296
   4-fold covers : {12,4,2,9}*1728b, {12,4,2,9}*1728c, {3,4,2,36}*1728, {3,8,2,9}*1728, {3,4,2,18}*1728, {6,4,2,9}*1728, {6,4,2,18}*1728b, {6,4,2,18}*1728c
Permutation Representation (GAP) :
s0 := (3,4);;
s1 := (2,3);;
s2 := (1,2)(3,4);;
s3 := ( 6, 7)( 8, 9)(10,11)(12,13);;
s4 := ( 5, 6)( 7, 8)( 9,10)(11,12);;
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, 
s0*s3*s0*s3, s1*s3*s1*s3, s2*s3*s2*s3, 
s0*s4*s0*s4, s1*s4*s1*s4, s2*s4*s2*s4, 
s0*s1*s0*s1*s0*s1, s1*s2*s1*s2*s1*s2*s1*s2, 
s0*s2*s1*s0*s2*s1*s0*s2*s1, s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4 ];;
poly := F / rels;;
 
Permutation Representation (Magma) :
s0 := Sym(13)!(3,4);
s1 := Sym(13)!(2,3);
s2 := Sym(13)!(1,2)(3,4);
s3 := Sym(13)!( 6, 7)( 8, 9)(10,11)(12,13);
s4 := Sym(13)!( 5, 6)( 7, 8)( 9,10)(11,12);
poly := sub<Sym(13)|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, s0*s3*s0*s3, 
s1*s3*s1*s3, s2*s3*s2*s3, s0*s4*s0*s4, 
s1*s4*s1*s4, s2*s4*s2*s4, s0*s1*s0*s1*s0*s1, 
s1*s2*s1*s2*s1*s2*s1*s2, s0*s2*s1*s0*s2*s1*s0*s2*s1, 
s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4*s3*s4 >; 
 

to this polytope