Part of the Atlas of Small Regular Polytopes

Polytope of Type {4,12}

Atlas Canonical Name {4,12}*96c

▶ Play as a twisty puzzle

Overview

Group
SmallGroup(96,187)
Rank
3
Schläfli Type
{4,12}
Vertices, edges, …
4, 24, 12
Order of s0s1s2
12
Order of s0s1s2s1
4
Also known as
if this polytope has a name.

Special Properties

  • Compact Hyperbolic Quotient
  • Locally Spherical
  • Non-Orientable
  • Flat

Quotients maximal quotients in bold

2-fold

4-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 := ( 1,21)( 2,13)( 3,10)( 4,35)( 5,36)( 6, 7)( 8,27)( 9,28)(11,22)(12,23)(14,19)(15,20)(16,47)(17,48)(18,46)(24,42)(25,44)(26,40)(29,45)(30,43)(31,41)(32,39)(33,37)(34,38);;
s1 := ( 2, 3)( 4, 5)( 6,16)( 8,12)( 9,11)(10,24)(13,29)(14,32)(15,17)(18,34)(19,20)(21,37)(22,40)(23,30)(25,28)(26,44)(27,41)(31,43)(35,46)(36,38)(39,48)(42,45);;
s2 := ( 1, 9)( 2, 5)( 3,20)( 4, 8)( 6,23)( 7,12)(10,15)(11,19)(13,36)(14,22)(16,26)(17,43)(18,29)(21,28)(24,39)(25,34)(27,35)(30,48)(31,37)(32,42)(33,41)(38,44)(40,47)(45,46);;
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*s2*s1*s0*s1*s2*s1*s2*s1, 
s2*s1*s2*s0*s1*s2*s0*s1*s2*s0*s1*s2*s1*s2*s1 ];;
poly := F / rels;;
Permutation Representation (Magma) 
s0 := Sym(48)!( 1,21)( 2,13)( 3,10)( 4,35)( 5,36)( 6, 7)( 8,27)( 9,28)(11,22)(12,23)(14,19)(15,20)(16,47)(17,48)(18,46)(24,42)(25,44)(26,40)(29,45)(30,43)(31,41)(32,39)(33,37)(34,38);
s1 := Sym(48)!( 2, 3)( 4, 5)( 6,16)( 8,12)( 9,11)(10,24)(13,29)(14,32)(15,17)(18,34)(19,20)(21,37)(22,40)(23,30)(25,28)(26,44)(27,41)(31,43)(35,46)(36,38)(39,48)(42,45);
s2 := Sym(48)!( 1, 9)( 2, 5)( 3,20)( 4, 8)( 6,23)( 7,12)(10,15)(11,19)(13,36)(14,22)(16,26)(17,43)(18,29)(21,28)(24,39)(25,34)(27,35)(30,48)(31,37)(32,42)(33,41)(38,44)(40,47)(45,46);
poly := sub<Sym(48)|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*s2*s1*s0*s1*s2*s1*s2*s1, 
s2*s1*s2*s0*s1*s2*s0*s1*s2*s0*s1*s2*s1*s2*s1 >;

References

None.

to this polytope.

Twisty Puzzle