Part of the Atlas of Small Regular Polytopes

Polytope of Type {4,20}

Atlas Canonical Name {4,20}*960c

▶ Play as a twisty puzzle

Overview

Group
SmallGroup(960,10871)
Rank
3
Schläfli Type
{4,20}
Vertices, edges, …
24, 240, 120
Order of s0s1s2
12
Order of s0s1s2s1
6
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

60-fold

120-fold

Covers minimal covers in bold

2-fold

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*s1*s2*s1*s0*(s2*s1)^3*s2> of order 2

60 facets

12 vertex figures

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

60 facets

12 vertex figures

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

64 facets

12 vertex figures

P/N, where N=<(s0*s1)^2, s2*s1*s0*s1*s2*s1*s0*(s2*s1)^3*s2> of order 4

36 facets

6 vertex figures

Representations

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

References

None.

to this polytope.

Twisty Puzzle