Part of the Atlas of Small Regular Polytopes

Polytope of Type {4,10}

Atlas Canonical Name {4,10}*1280a

▶ Play as a twisty puzzle

Overview

Group
SmallGroup(1280,1116442)
Rank
3
Schläfli Type
{4,10}
Vertices, edges, …
64, 320, 160
Order of s0s1s2
20
Order of s0s1s2s1
4
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

16-fold

32-fold

64-fold

80-fold

160-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=<(s1*s0*s2)^2*s1*s0*(s1*s2)^2*s1> of order 2

80 facets

32 vertex figures

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

96 facets

32 vertex figures

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

80 facets

32 vertex figures

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

80 facets

32 vertex figures

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

80 facets

32 vertex figures

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

80 facets

48 vertex figures

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

80 facets

32 vertex figures

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

80 facets

32 vertex figures

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

80 facets

32 vertex figures

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

80 facets

32 vertex figures

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

80 facets

32 vertex figures

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

80 facets

32 vertex figures

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

40 facets

16 vertex figures

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

40 facets

16 vertex figures

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

40 facets

16 vertex figures

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

40 facets

16 vertex figures

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

48 facets

16 vertex figures

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

40 facets

16 vertex figures

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

40 facets

16 vertex figures

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

48 facets

16 vertex figures

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

40 facets

16 vertex figures

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

40 facets

16 vertex figures

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

48 facets

16 vertex figures

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

40 facets

16 vertex figures

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

40 facets

16 vertex figures

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

48 facets

16 vertex figures

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

56 facets

16 vertex figures

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

40 facets

16 vertex figures

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

40 facets

16 vertex figures

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

48 facets

16 vertex figures

P/N, where N=<s1*s0*s1*s2*s1*s0*s2*s1*s2> of order 4

40 facets

16 vertex figures

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

40 facets

16 vertex figures

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

40 facets

16 vertex figures

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

40 facets

16 vertex figures

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

40 facets

16 vertex figures

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

40 facets

16 vertex figures

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

48 facets

16 vertex figures

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

40 facets

16 vertex figures

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

40 facets

16 vertex figures

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

48 facets

16 vertex figures

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

40 facets

16 vertex figures

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

40 facets

16 vertex figures

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

40 facets

16 vertex figures

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

40 facets

16 vertex figures

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

40 facets

16 vertex figures

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

40 facets

16 vertex figures

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

40 facets

16 vertex figures

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

40 facets

16 vertex figures

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

40 facets

16 vertex figures

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

40 facets

16 vertex figures

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

48 facets

16 vertex figures

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

48 facets

16 vertex figures

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

40 facets

16 vertex figures

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

40 facets

16 vertex figures

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

40 facets

16 vertex figures

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

48 facets

16 vertex figures

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

40 facets

16 vertex figures

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

40 facets

16 vertex figures

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

56 facets

16 vertex figures

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

40 facets

16 vertex figures

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

48 facets

24 vertex figures

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

40 facets

16 vertex figures

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

40 facets

16 vertex figures

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

40 facets

16 vertex figures

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

40 facets

16 vertex figures

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

40 facets

16 vertex figures

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

40 facets

24 vertex figures

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

40 facets

16 vertex figures

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

48 facets

16 vertex figures

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

40 facets

16 vertex figures

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

40 facets

16 vertex figures

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

48 facets

16 vertex figures

P/N, where N=<(s1*s0*s1*s2)^2, (s1*s2)^5> of order 4

40 facets

24 vertex figures

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

40 facets

24 vertex figures

P/N, where N=<(s1*s2)^5, (s0*s2*s1)^3*s0*(s2*s1)^2> of order 4

40 facets

24 vertex figures

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

40 facets

16 vertex figures

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

40 facets

16 vertex figures

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

40 facets

16 vertex figures

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

32 facets

16 vertex figures

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

20 facets

8 vertex figures

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

24 facets

8 vertex figures

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

20 facets

8 vertex figures

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

24 facets

8 vertex figures

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

20 facets

8 vertex figures

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

24 facets

8 vertex figures

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

20 facets

8 vertex figures

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

20 facets

8 vertex figures

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

20 facets

8 vertex figures

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

20 facets

8 vertex figures

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

20 facets

8 vertex figures

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

20 facets

8 vertex figures

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

20 facets

8 vertex figures

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

20 facets

8 vertex figures

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

20 facets

8 vertex figures

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

20 facets

8 vertex figures

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

28 facets

8 vertex figures

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

20 facets

8 vertex figures

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

20 facets

8 vertex figures

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

24 facets

8 vertex figures

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

20 facets

8 vertex figures

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

24 facets

8 vertex figures

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

24 facets

8 vertex figures

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

20 facets

8 vertex figures

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

24 facets

8 vertex figures

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

28 facets

8 vertex figures

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

24 facets

8 vertex figures

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

20 facets

8 vertex figures

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

28 facets

8 vertex figures

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

20 facets

8 vertex figures

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

20 facets

8 vertex figures

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

20 facets

8 vertex figures

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

24 facets

8 vertex figures

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

20 facets

8 vertex figures

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

24 facets

8 vertex figures

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

24 facets

12 vertex figures

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

20 facets

12 vertex figures

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

20 facets

12 vertex figures

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

20 facets

12 vertex figures

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

28 facets

12 vertex figures

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

24 facets

12 vertex figures

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

24 facets

12 vertex figures

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

20 facets

12 vertex figures

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

20 facets

12 vertex figures

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

20 facets

12 vertex figures

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

20 facets

8 vertex figures

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

24 facets

8 vertex figures

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

20 facets

8 vertex figures

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

20 facets

8 vertex figures

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

20 facets

8 vertex figures

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

24 facets

8 vertex figures

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

24 facets

8 vertex figures

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

20 facets

8 vertex figures

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

20 facets

8 vertex figures

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

24 facets

12 vertex figures

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

20 facets

8 vertex figures

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

28 facets

8 vertex figures

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

24 facets

8 vertex figures

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

32 facets

8 vertex figures

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

24 facets

8 vertex figures

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

20 facets

8 vertex figures

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

20 facets

8 vertex figures

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

24 facets

8 vertex figures

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

20 facets

8 vertex figures

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

28 facets

12 vertex figures

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

28 facets

8 vertex figures

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

24 facets

8 vertex figures

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

20 facets

8 vertex figures

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

28 facets

8 vertex figures

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

32 facets

8 vertex figures

P/N, where N=<(s0*s1)^2, s0*s2*s1*s0*s1*s2, (s0*s1*s2*s1)^2, (s1*s2)^5> of order 16

16 facets

6 vertex figures

P/N, where N=<(s0*s1*s2*s1)^2, (s1*s0*s1*s2)^2, (s2*s1*s0)^2*(s1*s2)^2, (s0*(s1*s2)^2*s1)^2> of order 16

14 facets

4 vertex figures

P/N, where N=<(s0*s1)^2, s0*s2*s1*s0*s1*s2, s0*(s2*s1)^2*s0*(s1*s2)^2, s1*(s2*s1*s0)^2*(s1*s2)^2*s1> of order 16

18 facets

4 vertex figures

P/N, where N=<(s1*s0*s1*s2)^2, s1*s0*s2*s1*s0*s1*s2*s1, (s2*s1*s0)^2*(s1*s2)^2, (s0*(s1*s2)^2*s1)^2> of order 16

14 facets

4 vertex figures

P/N, where N=<(s1*s0*s1*s2)^2, s1*s0*s2*s1*s0*s1*s2*s1, (s2*s1*s0)^2*(s1*s2)^2, s0*(s1*s2)^2*s1*s0*(s1*s2)^3> of order 16

14 facets

4 vertex figures

P/N, where N=<(s1*s0*s1*s2)^2, s0*s1*s2*s1*s0*(s1*s2)^2, s1*s0*(s2*s1)^2*s0*(s1*s2)^2*s1> of order 16

10 facets

4 vertex figures

P/N, where N=<(s0*s1*s2*s1)^2, (s1*s0*s1*s2)^2, s1*s0*(s2*s1)^2*s0*(s1*s2)^2*s1, s0*(s1*s2)^3*s1*s0*(s1*s2)^2> of order 16

10 facets

4 vertex figures

P/N, where N=<(s1*s0*s1*s2)^2, s1*s0*s2*s1*s0*s1*s2*s1, (s1*s2)^5, (s0*(s1*s2)^2*s1)^2> of order 16

12 facets

6 vertex figures

P/N, where N=<(s1*s0*s1*s2)^2, s1*s0*s2*s1*s0*s1*s2*s1, s0*(s2*s1)^2*s0*(s1*s2)^2, (s1*s2)^5> of order 16

12 facets

6 vertex figures

P/N, where N=<(s0*s1)^2, s0*s2*s1*s0*s1*s2, (s1*s2)^5, s1*(s2*s1*s0)^2*(s1*s2)^2*s1> of order 16

16 facets

6 vertex figures

P/N, where N=<(s1*s0*s1*s2)^2, s0*s1*s2*s1*s0*(s1*s2)^2, s1*s0*(s2*s1)^2*s0*(s1*s2)^3> of order 16

10 facets

4 vertex figures

P/N, where N=<(s0*s1)^2, s0*s2*s1*s0*s1*s2, s0*(s1*s2)^2*s1*s0*(s1*s2)^3> of order 16

14 facets

4 vertex figures

Representations

Permutation Representation (GAP)
s0 := (  1, 61)(  2, 62)(  3, 64)(  4, 63)(  5, 57)(  6, 58)(  7, 60)(  8, 59)(  9, 53)( 10, 54)( 11, 56)( 12, 55)( 13, 49)( 14, 50)( 15, 52)( 16, 51)( 17, 45)( 18, 46)( 19, 48)( 20, 47)( 21, 41)( 22, 42)( 23, 44)( 24, 43)( 25, 37)( 26, 38)( 27, 40)( 28, 39)( 29, 33)( 30, 34)( 31, 36)( 32, 35)( 65,125)( 66,126)( 67,128)( 68,127)( 69,121)( 70,122)( 71,124)( 72,123)( 73,117)( 74,118)( 75,120)( 76,119)( 77,113)( 78,114)( 79,116)( 80,115)( 81,109)( 82,110)( 83,112)( 84,111)( 85,105)( 86,106)( 87,108)( 88,107)( 89,101)( 90,102)( 91,104)( 92,103)( 93, 97)( 94, 98)( 95,100)( 96, 99);;
s1 := (  1,  3)(  2,  4)(  5,  7)(  6,  8)(  9, 99)( 10,100)( 11, 97)( 12, 98)( 13,103)( 14,104)( 15,101)( 16,102)( 17, 59)( 18, 60)( 19, 57)( 20, 58)( 21, 63)( 22, 64)( 23, 61)( 24, 62)( 25, 91)( 26, 92)( 27, 89)( 28, 90)( 29, 95)( 30, 96)( 31, 93)( 32, 94)( 33, 75)( 34, 76)( 35, 73)( 36, 74)( 37, 79)( 38, 80)( 39, 77)( 40, 78)( 41, 43)( 42, 44)( 45, 47)( 46, 48)( 49,115)( 50,116)( 51,113)( 52,114)( 53,119)( 54,120)( 55,117)( 56,118)( 65, 67)( 66, 68)( 69, 71)( 70, 72)( 81,123)( 82,124)( 83,121)( 84,122)( 85,127)( 86,128)( 87,125)( 88,126)(105,107)(106,108)(109,111)(110,112);;
s2 := ( 17, 25)( 18, 26)( 19, 27)( 20, 28)( 21, 29)( 22, 30)( 23, 31)( 24, 32)( 33, 41)( 34, 42)( 35, 43)( 36, 44)( 37, 45)( 38, 46)( 39, 47)( 40, 48)( 65,121)( 66,122)( 67,123)( 68,124)( 69,125)( 70,126)( 71,127)( 72,128)( 73,113)( 74,114)( 75,115)( 76,116)( 77,117)( 78,118)( 79,119)( 80,120)( 81, 97)( 82, 98)( 83, 99)( 84,100)( 85,101)( 86,102)( 87,103)( 88,104)( 89,105)( 90,106)( 91,107)( 92,108)( 93,109)( 94,110)( 95,111)( 96,112);;
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*s2*s1*s0*s1*s2*s1*s0*s1*s2*s1*s0*s1*s2*s1, 
s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2, 
s2*s0*s1*s2*s1*s2*s1*s2*s1*s2*s0*s1*s2*s0*s1*s2*s1*s2*s1*s2*s1*s2*s0*s1 ];;
poly := F / rels;;
Permutation Representation (Magma)
s0 := Sym(128)!(  1, 61)(  2, 62)(  3, 64)(  4, 63)(  5, 57)(  6, 58)(  7, 60)(  8, 59)(  9, 53)( 10, 54)( 11, 56)( 12, 55)( 13, 49)( 14, 50)( 15, 52)( 16, 51)( 17, 45)( 18, 46)( 19, 48)( 20, 47)( 21, 41)( 22, 42)( 23, 44)( 24, 43)( 25, 37)( 26, 38)( 27, 40)( 28, 39)( 29, 33)( 30, 34)( 31, 36)( 32, 35)( 65,125)( 66,126)( 67,128)( 68,127)( 69,121)( 70,122)( 71,124)( 72,123)( 73,117)( 74,118)( 75,120)( 76,119)( 77,113)( 78,114)( 79,116)( 80,115)( 81,109)( 82,110)( 83,112)( 84,111)( 85,105)( 86,106)( 87,108)( 88,107)( 89,101)( 90,102)( 91,104)( 92,103)( 93, 97)( 94, 98)( 95,100)( 96, 99);
s1 := Sym(128)!(  1,  3)(  2,  4)(  5,  7)(  6,  8)(  9, 99)( 10,100)( 11, 97)( 12, 98)( 13,103)( 14,104)( 15,101)( 16,102)( 17, 59)( 18, 60)( 19, 57)( 20, 58)( 21, 63)( 22, 64)( 23, 61)( 24, 62)( 25, 91)( 26, 92)( 27, 89)( 28, 90)( 29, 95)( 30, 96)( 31, 93)( 32, 94)( 33, 75)( 34, 76)( 35, 73)( 36, 74)( 37, 79)( 38, 80)( 39, 77)( 40, 78)( 41, 43)( 42, 44)( 45, 47)( 46, 48)( 49,115)( 50,116)( 51,113)( 52,114)( 53,119)( 54,120)( 55,117)( 56,118)( 65, 67)( 66, 68)( 69, 71)( 70, 72)( 81,123)( 82,124)( 83,121)( 84,122)( 85,127)( 86,128)( 87,125)( 88,126)(105,107)(106,108)(109,111)(110,112);
s2 := Sym(128)!( 17, 25)( 18, 26)( 19, 27)( 20, 28)( 21, 29)( 22, 30)( 23, 31)( 24, 32)( 33, 41)( 34, 42)( 35, 43)( 36, 44)( 37, 45)( 38, 46)( 39, 47)( 40, 48)( 65,121)( 66,122)( 67,123)( 68,124)( 69,125)( 70,126)( 71,127)( 72,128)( 73,113)( 74,114)( 75,115)( 76,116)( 77,117)( 78,118)( 79,119)( 80,120)( 81, 97)( 82, 98)( 83, 99)( 84,100)( 85,101)( 86,102)( 87,103)( 88,104)( 89,105)( 90,106)( 91,107)( 92,108)( 93,109)( 94,110)( 95,111)( 96,112);
poly := sub<Sym(128)|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*s2*s1*s0*s1*s2*s1*s0*s1*s2*s1*s0*s1*s2*s1, 
s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2, 
s2*s0*s1*s2*s1*s2*s1*s2*s1*s2*s0*s1*s2*s0*s1*s2*s1*s2*s1*s2*s1*s2*s0*s1 >; 

References

None.

to this polytope.

Twisty Puzzle