Part of the Atlas of Small Regular Polytopes

Polytope of Type {3,10}

Atlas Canonical Name {3,10}*120b

▶ Play as a twisty puzzle

Overview

Group
SmallGroup(120,35)
Rank
3
Schläfli Type
{3,10}
Vertices, edges, …
6, 30, 20
Order of s0s1s2
10
Order of s0s1s2s1
10
Also known as
if this polytope has a name.

Special Properties

  • Compact Hyperbolic Quotient
  • Locally Spherical
  • Non-Orientable

Quotients maximal quotients in bold

2-fold

Covers minimal covers in bold

2-fold

4-fold

6-fold

8-fold

10-fold

12-fold

14-fold

16-fold

Irregular Quotients of which this is a minimal cover

None.

Representations

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

References

None.

to this polytope.

Twisty Puzzle