Part of the Atlas of Small Regular Polytopes

Polytope of Type {6,10}

Atlas Canonical Name {6,10}*1920c

▶ Play as a twisty puzzle

Overview

Group
SmallGroup(1920,240997)
Rank
3
Schläfli Type
{6,10}
Vertices, edges, …
96, 480, 160
Order of s0s1s2
10
Order of s0s1s2s1
5
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

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

80 facets

48 vertex figures

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

80 facets

48 vertex figures

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

88 facets

48 vertex figures

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

56 facets

32 vertex figures

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

48 facets

24 vertex figures

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

44 facets

24 vertex figures

Representations

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

References

None.

to this polytope.

Twisty Puzzle