Part of the Atlas of Small Regular Polytopes

Polytope of Type {12,2,4,9}

Atlas Canonical Name {12,2,4,9}*1728

Overview

Group
SmallGroup(1728,30229)
Rank
5
Schläfli Type
{12,2,4,9}
Vertices, edges, …
12, 12, 4, 18, 9
Order of s0s1s2s3s4
36
Order of s0s1s2s3s4s3s2s1
2
Also known as
if this polytope has a name.

Special Properties

  • Degenerate
  • Universal
  • Non-Orientable
  • Flat

Quotients maximal quotients in bold

2-fold

3-fold

4-fold

6-fold

9-fold

12-fold

18-fold

Covers minimal covers in bold

None in this atlas.

Representations

Permutation Representation (GAP) 
s0 := ( 2, 3)( 4, 5)( 7,10)( 8, 9)(11,12);;
s1 := ( 1, 7)( 2, 4)( 3,11)( 5, 8)( 6, 9)(10,12);;
s2 := (14,19)(15,21)(16,23)(17,25)(20,30)(22,32)(26,36)(33,42)(35,44)(37,45)(39,46)(41,47);;
s3 := (13,14)(15,18)(16,17)(19,27)(20,26)(21,28)(22,24)(23,25)(29,35)(30,36)(31,33)(32,34)(37,43)(38,44)(39,41)(40,42)(45,48)(46,47);;
s4 := (13,18)(14,16)(15,26)(17,22)(19,23)(20,35)(21,36)(24,31)(25,32)(27,28)(29,43)(30,44)(33,39)(34,40)(37,41)(38,48)(42,46)(45,47);;
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, 
s0*s4*s0*s4, s1*s4*s1*s4, s2*s4*s2*s4, 
s2*s3*s2*s3*s2*s3*s2*s3, s2*s3*s4*s3*s2*s3*s4*s2*s3, 
s3*s4*s3*s4*s3*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*s0*s1*s0*s1*s0*s1 ];;
poly := F / rels;;
Permutation Representation (Magma) 
s0 := Sym(48)!( 2, 3)( 4, 5)( 7,10)( 8, 9)(11,12);
s1 := Sym(48)!( 1, 7)( 2, 4)( 3,11)( 5, 8)( 6, 9)(10,12);
s2 := Sym(48)!(14,19)(15,21)(16,23)(17,25)(20,30)(22,32)(26,36)(33,42)(35,44)(37,45)(39,46)(41,47);
s3 := Sym(48)!(13,14)(15,18)(16,17)(19,27)(20,26)(21,28)(22,24)(23,25)(29,35)(30,36)(31,33)(32,34)(37,43)(38,44)(39,41)(40,42)(45,48)(46,47);
s4 := Sym(48)!(13,18)(14,16)(15,26)(17,22)(19,23)(20,35)(21,36)(24,31)(25,32)(27,28)(29,43)(30,44)(33,39)(34,40)(37,41)(38,48)(42,46)(45,47);
poly := sub<Sym(48)|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, s0*s4*s0*s4, 
s1*s4*s1*s4, s2*s4*s2*s4, s2*s3*s2*s3*s2*s3*s2*s3, 
s2*s3*s4*s3*s2*s3*s4*s2*s3, s3*s4*s3*s4*s3*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*s0*s1*s0*s1*s0*s1 >;