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