Polytope of Type {4,20} with group SmallGroup(1280,1116442)

Overview

Group: SmallGroup(1280,1116442)
Rank: 3
Schläfli Type: {4,20}
Vertices, edges, …: 32, 320, 160
Order of s₀s₁s₂: 10
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

{4,10}*640b

4-fold

8-fold

{4,5}*160

32-fold

{2,10}*40

64-fold

{2,5}*20

160-fold

{2,2}*8

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

80 of {4}*8

16 vertex figures

16 of {20}*40

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

96 facets

64 of {4}*8
32 of {2}*4

16 vertex figures

16 of {20}*40

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

80 facets

80 of {4}*8

16 vertex figures

16 of {20}*40

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

80 facets

80 of {4}*8

16 vertex figures

16 of {20}*40

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

80 of {4}*8

16 vertex figures

16 of {20}*40

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

80 facets

80 of {4}*8

16 vertex figures

16 of {20}*40

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

80 facets

80 of {4}*8

16 vertex figures

16 of {20}*40

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

80 facets

80 of {4}*8

16 vertex figures

16 of {20}*40

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

80 facets

80 of {4}*8

16 vertex figures

16 of {20}*40

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

80 facets

80 of {4}*8

16 vertex figures

16 of {20}*40

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

80 facets

80 of {4}*8

16 vertex figures

16 of {20}*40

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

40 of {4}*8

8 vertex figures

8 of {20}*40

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

48 facets

32 of {4}*8
16 of {2}*4

8 vertex figures

8 of {20}*40

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

40 facets

40 of {4}*8

8 vertex figures

8 of {20}*40

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

40 of {4}*8

8 vertex figures

8 of {20}*40

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

32 of {4}*8
16 of {2}*4

8 vertex figures

8 of {20}*40

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

56 facets

32 of {2}*4
24 of {4}*8

8 vertex figures

8 of {20}*40

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

40 of {4}*8

8 vertex figures

8 of {20}*40

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

48 facets

32 of {4}*8
16 of {2}*4

8 vertex figures

8 of {20}*40

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

40 of {4}*8

8 vertex figures

8 of {20}*40

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

32 of {4}*8
16 of {2}*4

8 vertex figures

8 of {20}*40

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

40 of {4}*8

8 vertex figures

8 of {20}*40

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

40 facets

40 of {4}*8

8 vertex figures

8 of {20}*40

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

40 facets

40 of {4}*8

8 vertex figures

8 of {20}*40

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

40 facets

40 of {4}*8

8 vertex figures

8 of {20}*40

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

40 facets

40 of {4}*8

8 vertex figures

8 of {20}*40

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

40 of {4}*8

8 vertex figures

8 of {20}*40

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

40 of {4}*8

8 vertex figures

8 of {20}*40

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

40 of {4}*8

8 vertex figures

8 of {20}*40

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

32 of {4}*8
16 of {2}*4

8 vertex figures

8 of {20}*40

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

40 facets

40 of {4}*8

8 vertex figures

8 of {20}*40

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

40 facets

40 of {4}*8

8 vertex figures

8 of {20}*40

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

40 facets

40 of {4}*8

8 vertex figures

8 of {20}*40

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

40 facets

40 of {4}*8

8 vertex figures

8 of {20}*40

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

48 facets

16 of {2}*4
32 of {4}*8

8 vertex figures

8 of {20}*40

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

40 of {4}*8

8 vertex figures

8 of {20}*40

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

40 of {4}*8

8 vertex figures

8 of {20}*40

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

56 facets

24 of {4}*8
32 of {2}*4

8 vertex figures

8 of {20}*40

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

48 facets

32 of {4}*8
16 of {2}*4

8 vertex figures

8 of {20}*40

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

40 facets

40 of {4}*8

8 vertex figures

8 of {20}*40

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

40 facets

40 of {4}*8

8 vertex figures

8 of {20}*40

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

40 facets

40 of {4}*8

8 vertex figures

8 of {20}*40

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

48 facets

32 of {4}*8
16 of {2}*4

8 vertex figures

8 of {20}*40

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

40 facets

40 of {4}*8

8 vertex figures

8 of {20}*40

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

40 of {4}*8

8 vertex figures

8 of {20}*40

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

40 facets

40 of {4}*8

8 vertex figures

8 of {20}*40

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

40 facets

40 of {4}*8

8 vertex figures

8 of {20}*40

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

40 of {4}*8

8 vertex figures

8 of {20}*40

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

40 of {4}*8

8 vertex figures

8 of {20}*40

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

40 facets

40 of {4}*8

8 vertex figures

8 of {20}*40

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

48 facets

32 of {4}*8
16 of {2}*4

8 vertex figures

8 of {20}*40

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

40 of {4}*8

8 vertex figures

8 of {20}*40

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

40 of {4}*8

8 vertex figures

8 of {20}*40

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

32 of {4}*8
16 of {2}*4

8 vertex figures

8 of {20}*40

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

40 facets

40 of {4}*8

8 vertex figures

8 of {20}*40

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

40 of {4}*8

8 vertex figures

8 of {20}*40

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

16 of {4}*8
8 of {2}*4

4 vertex figures

4 of {20}*40

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

24 facets

16 of {4}*8
8 of {2}*4

4 vertex figures

4 of {20}*40

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

20 of {4}*8

4 vertex figures

4 of {20}*40

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

20 of {4}*8

4 vertex figures

4 of {20}*40

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

16 of {4}*8
8 of {2}*4

4 vertex figures

4 of {20}*40

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

16 of {4}*8
8 of {2}*4

4 vertex figures

4 of {20}*40

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

12 of {4}*8
16 of {2}*4

4 vertex figures

4 of {20}*40

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

20 of {4}*8

4 vertex figures

4 of {20}*40

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

16 of {4}*8
8 of {2}*4

4 vertex figures

4 of {20}*40

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

16 of {4}*8
8 of {2}*4

4 vertex figures

4 of {20}*40

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

24 facets

16 of {4}*8
8 of {2}*4

4 vertex figures

4 of {20}*40

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

24 of {2}*4
8 of {4}*8

4 vertex figures

4 of {20}*40

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

24 facets

16 of {4}*8
8 of {2}*4

4 vertex figures

4 of {20}*40

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

24 facets

16 of {4}*8
8 of {2}*4

4 vertex figures

4 of {20}*40

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

16 of {4}*8
8 of {2}*4

4 vertex figures

4 of {20}*40

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

28 facets

16 of {2}*4
12 of {4}*8

4 vertex figures

4 of {20}*40

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

20 facets

20 of {4}*8

4 vertex figures

4 of {20}*40

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

20 facets

20 of {4}*8

4 vertex figures

4 of {20}*40

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

20 facets

20 of {4}*8

4 vertex figures

4 of {20}*40

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

28 facets

12 of {4}*8
16 of {2}*4

4 vertex figures

4 of {20}*40

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

16 of {2}*4
12 of {4}*8

4 vertex figures

4 of {20}*40

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

32 facets

24 of {2}*4
8 of {4}*8

4 vertex figures

4 of {20}*40

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 := (  1,  5)(  2,  6)(  3,  8)(  4,  7)(  9, 13)( 10, 14)( 11, 16)( 12, 15)( 17, 29)( 18, 30)( 19, 32)( 20, 31)( 21, 25)( 22, 26)( 23, 28)( 24, 27)( 33, 45)( 34, 46)( 35, 48)( 36, 47)( 37, 41)( 38, 42)( 39, 44)( 40, 43)( 49, 53)( 50, 54)( 51, 56)( 52, 55)( 57, 61)( 58, 62)( 59, 64)( 60, 63)( 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)( 81,101)( 82,102)( 83,104)( 84,103)( 85, 97)( 86, 98)( 87,100)( 88, 99)( 89,109)( 90,110)( 91,112)( 92,111)( 93,105)( 94,106)( 95,108)( 96,107);;
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, 
s2*s0*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s0*s1*s2*s1*s2*s1*s2*s1*s2*s1, 
s0*s1*s2*s1*s2*s1*s0*s1*s2*s1*s2*s1*s0*s1*s2*s1*s2*s1*s0*s1*s2*s1*s2*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)!(  1,  5)(  2,  6)(  3,  8)(  4,  7)(  9, 13)( 10, 14)( 11, 16)( 12, 15)( 17, 29)( 18, 30)( 19, 32)( 20, 31)( 21, 25)( 22, 26)( 23, 28)( 24, 27)( 33, 45)( 34, 46)( 35, 48)( 36, 47)( 37, 41)( 38, 42)( 39, 44)( 40, 43)( 49, 53)( 50, 54)( 51, 56)( 52, 55)( 57, 61)( 58, 62)( 59, 64)( 60, 63)( 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)( 81,101)( 82,102)( 83,104)( 84,103)( 85, 97)( 86, 98)( 87,100)( 88, 99)( 89,109)( 90,110)( 91,112)( 92,111)( 93,105)( 94,106)( 95,108)( 96,107);
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, 
s2*s0*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s0*s1*s2*s1*s2*s1*s2*s1*s2*s1, 
s0*s1*s2*s1*s2*s1*s0*s1*s2*s1*s2*s1*s0*s1*s2*s1*s2*s1*s0*s1*s2*s1*s2*s1 >;

References

None.

to this polytope.

Overview

Special Properties

Related Polytopes

Quotients maximal quotients in bold

Covers minimal covers in bold

Irregular Quotients of which this is a minimal cover

Representations

References

Twisty Puzzle