Part of the Atlas of Small Regular Polytopes

Polytope of Type {12,6}

Atlas Canonical Name {12,6}*1440d

▶ Play as a twisty puzzle

Overview

Group
SmallGroup(1440,5849)
Rank
3
Schläfli Type
{12,6}
Vertices, edges, …
120, 360, 60
Order of s0s1s2
10
Order of s0s1s2s1
6
Also known as
if this polytope has a name.

Special Properties

  • Compact Hyperbolic Quotient
  • Locally Spherical
  • Orientable

Quotients maximal quotients in bold

2-fold

3-fold

6-fold

12-fold

180-fold

Covers minimal covers in bold

None in this atlas.

Irregular Quotients of which this is a minimal cover

Click an entry to reveal its facets and vertex figures.

P/N, where N=<(s0*s1)^2*(s2*s1)^2*s0*s2*s1*s0*(s2*s1)^2*s2> of order 2

30 facets

60 vertex figures

P/N, where N=<s0*s1*s0*(s2*s1)^2*(s0*s1)^2*s2*s1*s0*s2*s1*s2> of order 2

30 facets

60 vertex figures

P/N, where N=<(s0*s1*s2*s1)^2*s0*s2*s1*s2> of order 2

30 facets

60 vertex figures

P/N, where N=<(s1*s2)^3> of order 2

30 facets

66 vertex figures

P/N, where N=<s2*(s1*s0)^2*(s2*s1)^2*(s0*s2*s1)^2*s2> of order 2

32 facets

60 vertex figures

P/N, where N=<s0*s1*s0*s2*s1*s0*s1*s2*(s1*s0)^2*s2> of order 2

30 facets

60 vertex figures

P/N, where N=<(s0*s1)^6, s2*(s1*s0)^2*(s2*s1)^2*(s0*s2*s1)^2*s2> of order 4

18 facets

30 vertex figures

P/N, where N=<(s1*s2)^3, (s0*s1)^2*(s2*s1)^2*s0*s2*s1*s0> of order 4

16 facets

36 vertex figures

P/N, where N=<(s0*s1*s2*s1)^2*s0*s2*s1*s2, s0*s1*s0*s2*s1*s0*(s2*s1)^2*s0*s1*s0*s2> of order 4

16 facets

30 vertex figures

P/N, where N=<s0*s1*s0*s2*s1*s0*s1*s2*(s1*s0)^2*s2, s2*(s1*s0)^2*(s2*s1)^2*(s0*s2*s1)^2*s2> of order 4

16 facets

30 vertex figures

P/N, where N=<s1*s0*(s2*s1*s0*s1)^2*s2, s1*s2*s1*s0*(s2*s1)^2*(s0*s1)^2*s2*s1*s2> of order 4

16 facets

30 vertex figures

P/N, where N=<s1*s0*(s2*s1*s0*s1)^2*s2, (s0*s1)^6, s1*s2*s1*s0*(s2*s1)^2*(s0*s1)^2*s2*s1*s2> of order 8

9 facets

15 vertex figures

P/N, where N=<(s1*s2)^3, (s0*s1)^6> of order 8

9 facets

18 vertex figures

Representations

Permutation Representation (GAP) 
s0 := ( 1, 2)( 3, 5)( 4, 6)( 9,11);;
s1 := ( 2, 6)( 4, 5)( 8, 9)(10,11);;
s2 := (1,5)(2,3)(7,8);;
poly := Group([s0,s1,s2]);;
Finitely Presented Group Representation (GAP) 
F := FreeGroup("s0","s1","s2");;
s0 := F.1;;  s1 := F.2;;  s2 := F.3;;  
rels := [ s0*s0, s1*s1, s2*s2, s0*s2*s0*s2, s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2, 
s0*s1*s0*s1*s0*s1*s2*s0*s1*s0*s1*s0*s1*s0*s1*s2*s0*s1, 
s2*s0*s1*s2*s1*s2*s0*s1*s2*s1*s2*s0*s1*s2*s1*s2*s0*s1*s2*s1, 
s0*s1*s2*s1*s0*s1*s2*s1*s2*s0*s1*s0*s1*s2*s1*s0*s1*s2*s1*s2*s0*s1 ];;
poly := F / rels;;
Permutation Representation (Magma) 
s0 := Sym(11)!( 1, 2)( 3, 5)( 4, 6)( 9,11);
s1 := Sym(11)!( 2, 6)( 4, 5)( 8, 9)(10,11);
s2 := Sym(11)!(1,5)(2,3)(7,8);
poly := sub<Sym(11)|s0,s1,s2>;
Finitely Presented Group Representation (Magma) 
poly<s0,s1,s2> := Group< s0,s1,s2 | s0*s0, s1*s1, s2*s2, 
s0*s2*s0*s2, s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2, 
s0*s1*s0*s1*s0*s1*s2*s0*s1*s0*s1*s0*s1*s0*s1*s2*s0*s1, 
s2*s0*s1*s2*s1*s2*s0*s1*s2*s1*s2*s0*s1*s2*s1*s2*s0*s1*s2*s1, 
s0*s1*s2*s1*s0*s1*s2*s1*s2*s0*s1*s0*s1*s2*s1*s0*s1*s2*s1*s2*s0*s1 >;

References

None.

to this polytope.

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