Part of the Atlas of Small Regular Polytopes

Polytope of Type {12,2,6,6}

Atlas Canonical Name {12,2,6,6}*1728c

Overview

Group
SmallGroup(1728,47319)
Rank
5
Schläfli Type
{12,2,6,6}
Vertices, edges, …
12, 12, 6, 18, 6
Order of s0s1s2s3s4
12
Order of s0s1s2s3s4s3s2s1
2
Also known as
if this polytope has a name.

Special Properties

  • Degenerate
  • Universal
  • Orientable
  • Flat

Quotients maximal quotients in bold

2-fold

3-fold

4-fold

6-fold

8-fold

9-fold

12-fold

18-fold

24-fold

27-fold

36-fold

54-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 := (15,16)(17,18)(19,20)(21,22)(23,26)(24,25)(27,30)(28,29);;
s3 := (13,27)(14,23)(15,21)(16,29)(17,19)(18,28)(20,25)(22,24)(26,30);;
s4 := (17,18)(21,22)(23,24)(25,26)(27,28)(29,30);;
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, 
s4*s2*s3*s4*s3*s4*s2*s3*s4*s3, s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3, 
s2*s3*s2*s3*s4*s3*s2*s3*s2*s3*s4*s3, 
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(30)!( 2, 3)( 4, 5)( 7,10)( 8, 9)(11,12);
s1 := Sym(30)!( 1, 7)( 2, 4)( 3,11)( 5, 8)( 6, 9)(10,12);
s2 := Sym(30)!(15,16)(17,18)(19,20)(21,22)(23,26)(24,25)(27,30)(28,29);
s3 := Sym(30)!(13,27)(14,23)(15,21)(16,29)(17,19)(18,28)(20,25)(22,24)(26,30);
s4 := Sym(30)!(17,18)(21,22)(23,24)(25,26)(27,28)(29,30);
poly := sub<Sym(30)|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, s4*s2*s3*s4*s3*s4*s2*s3*s4*s3, 
s2*s3*s2*s3*s2*s3*s2*s3*s2*s3*s2*s3, 
s2*s3*s2*s3*s4*s3*s2*s3*s2*s3*s4*s3, 
s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1 >;