1Euclidean automorphism group of order 120 (possibly only approximation)
2Integrality not known
3************************************************************************
43 permutations of 12 vertices of polyhedron
5
6Perm 1: 1 2 4 3 7 8 5 6 10 9 11 12
7Perm 2: 1 3 2 5 4 6 7 9 8 11 10 12
8Perm 3: 2 1 3 4 6 5 8 7 9 10 12 11
9
10Cycle decompositions
11
12Perm 1: (3 4) (5 7) (6 8) (9 10) --
13Perm 2: (2 3) (4 5) (8 9) (10 11) --
14Perm 3: (1 2) (5 6) (7 8) (11 12) --
15
161 orbits of vertices of polyhedron
17
18Orbit 1 , length 12:  1 2 3 4 5 6 7 8 9 10 11 12
19
20************************************************************************
213 permutations of 20 support hyperplanes
22
23Perm 1: 2 1 5 6 3 4 7 8 11 12 9 10 13 14 17 18 15 16 20 19
24Perm 2: 1 3 2 4 7 9 5 10 6 8 13 15 11 16 12 14 17 19 18 20
25Perm 3: 1 2 4 3 6 5 8 7 10 9 12 11 14 13 16 15 18 17 19 20
26
27Cycle decompositions
28
29Perm 1: (1 2) (3 5) (4 6) (9 11) (10 12) (15 17) (16 18) (19 20) --
30Perm 2: (2 3) (5 7) (6 9) (8 10) (11 13) (12 15) (14 16) (18 19) --
31Perm 3: (3 4) (5 6) (7 8) (9 10) (11 12) (13 14) (15 16) (17 18) --
32
331 orbits of support hyperplanes
34
35Orbit 1 , length 20:  1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20
36
37