Part of the Atlas of Small Regular Polytopes

Polytope of Type {4,6}

Atlas Canonical Name {4,6}*192b

▶ Play as a twisty puzzle

Overview

Group
SmallGroup(192,1472)
Rank
3
Schläfli Type
{4,6}
Vertices, edges, …
16, 48, 24
Order of s0s1s2
12
Order of s0s1s2s1
4
Also known as
if this polytope has a name.

Special Properties

  • Compact Hyperbolic Quotient
  • Locally Spherical
  • Orientable

Quotients maximal quotients in bold

2-fold

4-fold

8-fold

12-fold

16-fold

24-fold

Covers minimal covers in bold

2-fold

3-fold

4-fold

5-fold

6-fold

7-fold

9-fold

10-fold

Irregular Quotients of which this is a minimal cover

Click an entry to reveal its facets and vertex figures.

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

12 facets

12 vertex figures

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

16 facets

8 vertex figures

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

12 facets

8 vertex figures

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

12 facets

8 vertex figures

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

8 facets

8 vertex figures

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

6 facets

4 vertex figures

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

8 facets

6 vertex figures

P/N, where N=<s0*s2*s1*s0*s1*s2, s1*s0*s2*s1*s0*s1*s2*s1> of order 4

10 facets

4 vertex figures

Representations

Permutation Representation (GAP) 
s0 := ( 5, 6)( 7, 8)( 9,10);;
s1 := ( 1, 7)( 2, 8)( 3,11)( 4,12)( 5, 9)( 6,10);;
s2 := ( 1, 3)( 2, 4)( 7, 9)( 8,10);;
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, s0*s1*s0*s1*s0*s1*s0*s1, 
s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2, 
s2*s0*s1*s2*s1*s2*s0*s1*s2*s0*s1*s2*s1*s2*s0*s1 ];;
poly := F / rels;;
Permutation Representation (Magma) 
s0 := Sym(12)!( 5, 6)( 7, 8)( 9,10);
s1 := Sym(12)!( 1, 7)( 2, 8)( 3,11)( 4,12)( 5, 9)( 6,10);
s2 := Sym(12)!( 1, 3)( 2, 4)( 7, 9)( 8,10);
poly := sub<Sym(12)|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, s0*s1*s0*s1*s0*s1*s0*s1, 
s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2, 
s2*s0*s1*s2*s1*s2*s0*s1*s2*s0*s1*s2*s1*s2*s0*s1 >;

References

None.

to this polytope.

Twisty Puzzle