Part of the Atlas of Small Regular Polytopes

Polytope of Type {12,4}

Atlas Canonical Name {12,4}*1920c

▶ Play as a twisty puzzle

Overview

Group
SmallGroup(1920,240996)
Rank
3
Schläfli Type
{12,4}
Vertices, edges, …
240, 480, 80
Order of s0s1s2
5
Order of s0s1s2s1
6
Also known as
if this polytope has a name.

Special Properties

  • Compact Hyperbolic Quotient
  • Locally Spherical
  • Non-Orientable

Quotients maximal quotients in bold

16-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)^3*(s2*(s1*s0)^2*s1)^2*s2> of order 2

40 facets

120 vertex figures

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

44 facets

120 vertex figures

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

28 facets

80 vertex figures

P/N, where N=<(s0*s1*s2*s1)^3, s1*s0*s2*(s1*s0)^5*s1*s2*s1> of order 4

26 facets

60 vertex figures

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

22 facets

60 vertex figures

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

26 facets

60 vertex figures

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

24 facets

60 vertex figures

P/N, where N=<(s0*s1*s2*s1)^3, (s1*s0)^2*s1*s2*s1*s0*s1*s2*(s1*s0)^2*s2*s1, s1*s0*s2*(s1*s0)^5*s1*s2*s1> of order 8

16 facets

30 vertex figures

P/N, where N=<(s0*s1*s2*s1)^3, (s0*s1)^2*s2*s1*s0*s1*s2*(s1*s0)^2*s2, s1*s0*s2*(s1*s0)^5*s1*s2*s1> of order 8

14 facets

30 vertex figures

P/N, where N=<(s0*s1)^2*s2*(s1*s0)^2*s2, (s0*s1*s2*s1)^3> of order 12

10 facets

20 vertex figures

Representations

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

References

None.

to this polytope.

Twisty Puzzle