Part of the Atlas of Small Regular Polytopes

Polytope of Type {20,12}

Atlas Canonical Name {20,12}*1920f

▶ Play as a twisty puzzle

Overview

Group
SmallGroup(1920,240505)
Rank
3
Schläfli Type
{20,12}
Vertices, edges, …
80, 480, 48
Order of s0s1s2
4
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

16-fold

60-fold

120-fold

240-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*s0*s2*(s1*s0)^2*(s2*s1)^2*s0*s2*s1> of order 2

24 facets

40 vertex figures

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

24 facets

40 vertex figures

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

24 facets

40 vertex figures

Representations

Permutation Representation (GAP) 
s0 := ( 1, 8)( 2, 4)( 3, 5)( 6, 7)(10,13)(11,12);;
s1 := ( 1, 4)( 2, 7)( 3, 8)( 5, 6)( 9,11)(10,12);;
s2 := ( 2, 4)( 3, 5)(10,13);;
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, s2*s0*s1*s2*s0*s1*s2*s0*s1*s2*s0*s1, 
s0*s1*s2*s1*s0*s1*s2*s1*s0*s1*s2*s1*s0*s1*s2*s1, 
s0*s1*s0*s1*s2*s1*s0*s1*s0*s1*s2*s1*s0*s1*s0*s1*s2*s1*s0*s1*s0*s1*s2*s1, 
s0*s1*s0*s1*s2*s1*s2*s1*s2*s1*s2*s1*s0*s1*s0*s1*s2*s1*s2*s1*s2*s1*s2*s1, 
s0*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s0*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1 ];;
poly := F / rels;;
Permutation Representation (Magma) 
s0 := Sym(13)!( 1, 8)( 2, 4)( 3, 5)( 6, 7)(10,13)(11,12);
s1 := Sym(13)!( 1, 4)( 2, 7)( 3, 8)( 5, 6)( 9,11)(10,12);
s2 := Sym(13)!( 2, 4)( 3, 5)(10,13);
poly := sub<Sym(13)|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, s2*s0*s1*s2*s0*s1*s2*s0*s1*s2*s0*s1, 
s0*s1*s2*s1*s0*s1*s2*s1*s0*s1*s2*s1*s0*s1*s2*s1, 
s0*s1*s0*s1*s2*s1*s0*s1*s0*s1*s2*s1*s0*s1*s0*s1*s2*s1*s0*s1*s0*s1*s2*s1, 
s0*s1*s0*s1*s2*s1*s2*s1*s2*s1*s2*s1*s0*s1*s0*s1*s2*s1*s2*s1*s2*s1*s2*s1, 
s0*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s0*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1 >;

References

None.

to this polytope.

Twisty Puzzle