Questions?
See the FAQ
or other info.

Polytope of Type {3,6,2,2}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {3,6,2,2}*432
if this polytope has a name.
Group : SmallGroup(432,545)
Rank : 5
Schlafli Type : {3,6,2,2}
Number of vertices, edges, etc : 9, 27, 18, 2, 2
Order of s0s1s2s3s4 : 6
Order of s0s1s2s3s4s3s2s1 : 2
Special Properties :
   Degenerate
   Universal
   Orientable
   Flat
Related Polytopes :
   Facet
   Vertex Figure
   Dual
Facet Of :
   {3,6,2,2,2} of size 864
   {3,6,2,2,3} of size 1296
   {3,6,2,2,4} of size 1728
Vertex Figure Of :
   {2,3,6,2,2} of size 864
   {4,3,6,2,2} of size 1728
Quotients (Maximal Quotients in Boldface) :
   3-fold quotients : {3,6,2,2}*144
   9-fold quotients : {3,2,2,2}*48
Covers (Minimal Covers in Boldface) :
   2-fold covers : {3,6,2,4}*864, {3,6,4,2}*864a, {6,6,2,2}*864c
   3-fold covers : {9,6,2,2}*1296a, {9,6,2,2}*1296b, {9,6,2,2}*1296c, {9,6,2,2}*1296d, {3,6,2,2}*1296, {3,18,2,2}*1296, {3,6,2,6}*1296, {3,6,6,2}*1296c
   4-fold covers : {3,6,2,8}*1728, {3,6,8,2}*1728a, {3,6,4,4}*1728a, {12,6,2,2}*1728a, {6,6,2,4}*1728c, {6,6,4,2}*1728c, {6,12,2,2}*1728c, {3,6,2,2}*1728, {3,12,2,2}*1728
Permutation Representation (GAP) :
s0 := (2,3)(4,7)(5,6);;
s1 := (1,4)(2,9)(5,8);;
s2 := (4,5)(6,7)(8,9);;
s3 := (10,11);;
s4 := (12,13);;
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, 
s3*s4*s3*s4, s0*s1*s0*s1*s0*s1, s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2, 
s2*s0*s1*s2*s0*s1*s2*s0*s1*s2*s0*s1*s2*s0*s1*s2*s0*s1 ];;
poly := F / rels;;
 
Permutation Representation (Magma) :
s0 := Sym(13)!(2,3)(4,7)(5,6);
s1 := Sym(13)!(1,4)(2,9)(5,8);
s2 := Sym(13)!(4,5)(6,7)(8,9);
s3 := Sym(13)!(10,11);
s4 := Sym(13)!(12,13);
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, s3*s4*s3*s4, 
s0*s1*s0*s1*s0*s1, s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2, 
s2*s0*s1*s2*s0*s1*s2*s0*s1*s2*s0*s1*s2*s0*s1*s2*s0*s1 >; 
 

to this polytope