Part of the Atlas of Small Regular Polytopes

Polytope of Type {12,4}

Atlas Canonical Name {12,4}*96a

▶ Play as a twisty puzzle

Overview

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

Special Properties

  • Compact Hyperbolic Quotient
  • Locally Spherical
  • Orientable
  • Flat
  • Self-Petrie

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, 3)( 4, 5)( 6,10)( 8,12)( 9,11)(15,20)(16,19)(17,18)(21,22)(23,24);;
s1 := ( 1, 8)( 2, 4)( 3,17)( 5, 9)( 6,23)( 7,11)(10,21)(12,18)(13,19)(14,15)(16,24)(20,22);;
s2 := ( 2, 6)( 3,10)( 8,15)( 9,16)(11,19)(12,20);;
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*s2*s1*s0*s1*s2*s1, 
s1*s2*s1*s2*s1*s2*s1*s2, 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(24)!( 2, 3)( 4, 5)( 6,10)( 8,12)( 9,11)(15,20)(16,19)(17,18)(21,22)(23,24);
s1 := Sym(24)!( 1, 8)( 2, 4)( 3,17)( 5, 9)( 6,23)( 7,11)(10,21)(12,18)(13,19)(14,15)(16,24)(20,22);
s2 := Sym(24)!( 2, 6)( 3,10)( 8,15)( 9,16)(11,19)(12,20);
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*s2*s1*s0*s1*s2*s1, 
s1*s2*s1*s2*s1*s2*s1*s2, s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1 >;

References

None.

to this polytope.

Twisty Puzzle