Part of the Atlas of Small Regular Polytopes

Polytope of Type {8,3}

Atlas Canonical Name {8,3}*1440

▶ Play as a twisty puzzle

Overview

Group
SmallGroup(1440,5843)
Rank
3
Schläfli Type
{8,3}
Vertices, edges, …
240, 360, 90
Order of s0s1s2
10
Order of s0s1s2s1
8
Also known as
if this polytope has a name.

Special Properties

  • Compact Hyperbolic Quotient
  • Locally Spherical
  • Orientable

Quotients maximal quotients in bold

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

46 facets

120 vertex figures

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

24 facets

60 vertex figures

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

23 facets

60 vertex figures

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

24 facets

60 vertex figures

P/N, where N=<(s0*s1)^3*s2*(s1*s0)^2*s2*s1*s0, (s0*s1)^4*s2*(s1*s0)^3*s2*s1*s0*s1*s2> of order 8

13 facets

30 vertex figures

Representations

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

References

None.

to this polytope.

Twisty Puzzle