Part of the Atlas of Small Regular Polytopes

Polytope of Type {4,12}

Atlas Canonical Name {4,12}*96a

▶ Play as a twisty puzzle

Overview

Group
SmallGroup(96,89)
Rank
3
Schläfli Type
{4,12}
Vertices, edges, …
4, 24, 12
Order of s0s1s2
12
Order of s0s1s2s1
2
Also known as
{4,12|2}. if this polytope has another name.

Special Properties

  • Compact Hyperbolic Quotient
  • Locally Spherical
  • Orientable
  • Flat

Quotients maximal quotients in bold

2-fold

3-fold

4-fold

6-fold

8-fold

12-fold

Covers minimal covers in bold

2-fold

3-fold

4-fold

5-fold

6-fold

7-fold

8-fold

9-fold

10-fold

11-fold

12-fold

13-fold

14-fold

15-fold

17-fold

18-fold

19-fold

20-fold

Irregular Quotients of which this is a minimal cover

None.

Representations

Permutation Representation (GAP) 
s0 := ( 2, 6)( 3,10)( 8,15)( 9,16)(11,19)(12,20);;
s1 := ( 1, 2)( 3, 7)( 4, 9)( 5, 8)( 6,14)(10,13)(11,18)(12,17)(15,24)(16,23)(19,22)(20,21);;
s2 := ( 1, 4)( 2,11)( 3, 8)( 6,19)( 7,17)( 9,12)(10,15)(13,21)(14,23)(16,20);;
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, 
s0*s1*s2*s1*s0*s1*s2*s1, s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2 ];;
poly := F / rels;;
Permutation Representation (Magma) 
s0 := Sym(24)!( 2, 6)( 3,10)( 8,15)( 9,16)(11,19)(12,20);
s1 := Sym(24)!( 1, 2)( 3, 7)( 4, 9)( 5, 8)( 6,14)(10,13)(11,18)(12,17)(15,24)(16,23)(19,22)(20,21);
s2 := Sym(24)!( 1, 4)( 2,11)( 3, 8)( 6,19)( 7,17)( 9,12)(10,15)(13,21)(14,23)(16,20);
poly := sub<Sym(24)|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, 
s0*s1*s2*s1*s0*s1*s2*s1, s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2 >;

References

None.

to this polytope.

Twisty Puzzle