E7 # Dynkin diagram 2 | 1---3---4---5---6---7 # coordinates (and numbering of) the positive co-roots 1 [1, 0, 0, 0, 0, 0, 0] 2 [0, 1, 0, 0, 0, 0, 0] 3 [0, 0, 1, 0, 0, 0, 0] 4 [0, 0, 0, 1, 0, 0, 0] 5 [0, 0, 0, 0, 1, 0, 0] 6 [0, 0, 0, 0, 0, 1, 0] 7 [0, 0, 0, 0, 0, 0, 1] 8 [1, 0, 1, 0, 0, 0, 0] 9 [0, 1, 0, 1, 0, 0, 0] 10 [0, 0, 1, 1, 0, 0, 0] 11 [0, 0, 0, 1, 1, 0, 0] 12 [0, 0, 0, 0, 1, 1, 0] 13 [0, 0, 0, 0, 0, 1, 1] 14 [1, 0, 1, 1, 0, 0, 0] 15 [0, 1, 1, 1, 0, 0, 0] 16 [0, 1, 0, 1, 1, 0, 0] 17 [0, 0, 1, 1, 1, 0, 0] 18 [0, 0, 0, 1, 1, 1, 0] 19 [0, 0, 0, 0, 1, 1, 1] 20 [1, 1, 1, 1, 0, 0, 0] 21 [1, 0, 1, 1, 1, 0, 0] 22 [0, 1, 1, 1, 1, 0, 0] 23 [0, 1, 0, 1, 1, 1, 0] 24 [0, 0, 1, 1, 1, 1, 0] 25 [0, 0, 0, 1, 1, 1, 1] 26 [1, 1, 1, 1, 1, 0, 0] 27 [1, 0, 1, 1, 1, 1, 0] 28 [0, 1, 1, 2, 1, 0, 0] 29 [0, 1, 1, 1, 1, 1, 0] 30 [0, 1, 0, 1, 1, 1, 1] 31 [0, 0, 1, 1, 1, 1, 1] 32 [1, 1, 1, 2, 1, 0, 0] 33 [1, 1, 1, 1, 1, 1, 0] 34 [1, 0, 1, 1, 1, 1, 1] 35 [0, 1, 1, 2, 1, 1, 0] 36 [0, 1, 1, 1, 1, 1, 1] 37 [1, 1, 2, 2, 1, 0, 0] 38 [1, 1, 1, 2, 1, 1, 0] 39 [1, 1, 1, 1, 1, 1, 1] 40 [0, 1, 1, 2, 2, 1, 0] 41 [0, 1, 1, 2, 1, 1, 1] 42 [1, 1, 2, 2, 1, 1, 0] 43 [1, 1, 1, 2, 2, 1, 0] 44 [1, 1, 1, 2, 1, 1, 1] 45 [0, 1, 1, 2, 2, 1, 1] 46 [1, 1, 2, 2, 2, 1, 0] 47 [1, 1, 2, 2, 1, 1, 1] 48 [1, 1, 1, 2, 2, 1, 1] 49 [0, 1, 1, 2, 2, 2, 1] 50 [1, 1, 2, 3, 2, 1, 0] 51 [1, 1, 2, 2, 2, 1, 1] 52 [1, 1, 1, 2, 2, 2, 1] 53 [1, 2, 2, 3, 2, 1, 0] 54 [1, 1, 2, 3, 2, 1, 1] 55 [1, 1, 2, 2, 2, 2, 1] 56 [1, 2, 2, 3, 2, 1, 1] 57 [1, 1, 2, 3, 2, 2, 1] 58 [1, 2, 2, 3, 2, 2, 1] 59 [1, 1, 2, 3, 3, 2, 1] 60 [1, 2, 2, 3, 3, 2, 1] 61 [1, 2, 2, 4, 3, 2, 1] 62 [1, 2, 3, 4, 3, 2, 1] 63 [2, 2, 3, 4, 3, 2, 1] # f-vector of the cell complex, first segregated by faces of the # dominant chamber, and then cumulative (q marks co-dimension): [0, 0, 0, 0, 0, 0, 0, 0] {1, 2, 3, 4, 5, 6, 7} [0, 0, 0, 0, 0, 0, 0, 1] {2, 3, 4, 5, 6, 7} [0, 0, 0, 0, 0, 0, 0, 2] {1, 3, 4, 5, 6, 7} [0, 0, 0, 0, 0, 0, 6, 1] {3, 4, 5, 6, 7} [0, 0, 0, 0, 0, 0, 0, 1] {1, 2, 4, 5, 6, 7} [0, 0, 0, 0, 0, 0, 4, 1] {2, 4, 5, 6, 7} [0, 0, 0, 0, 0, 0, 3, 1] {1, 4, 5, 6, 7} [0, 0, 0, 0, 0, 18, 9, 1] {4, 5, 6, 7} [0, 0, 0, 0, 0, 0, 0, 1] {1, 2, 3, 5, 6, 7} [0, 0, 0, 0, 0, 0, 2, 1] {2, 3, 5, 6, 7} [0, 0, 0, 0, 0, 0, 4, 1] {1, 3, 5, 6, 7} [0, 0, 0, 0, 0, 8, 7, 1] {3, 5, 6, 7} [0, 0, 0, 0, 0, 0, 1, 1] {1, 2, 5, 6, 7} [0, 0, 0, 0, 0, 11, 8, 1] {2, 5, 6, 7} [0, 0, 0, 0, 0, 5, 5, 1] {1, 5, 6, 7} [0, 0, 0, 0, 48, 43, 12, 1] {5, 6, 7} [0, 0, 0, 0, 0, 0, 0, 2] {1, 2, 3, 4, 6, 7} [0, 0, 0, 0, 0, 0, 5, 3] {2, 3, 4, 6, 7} [0, 0, 0, 0, 0, 0, 4, 1] {1, 3, 4, 6, 7} [0, 0, 0, 0, 0, 13, 13, 2] {3, 4, 6, 7} [0, 0, 0, 0, 0, 0, 1, 1] {1, 2, 4, 6, 7} [0, 0, 0, 0, 0, 11, 9, 1] {2, 4, 6, 7} [0, 0, 0, 0, 0, 1, 5, 1] {1, 4, 6, 7} [0, 0, 0, 0, 23, 44, 19, 2] {4, 6, 7} [0, 0, 0, 0, 0, 0, 1, 1] {1, 2, 3, 6, 7} [0, 0, 0, 0, 0, 3, 4, 1] {2, 3, 6, 7} [0, 0, 0, 0, 0, 6, 5, 1] {1, 3, 6, 7} [0, 0, 0, 0, 19, 35, 13, 1] {3, 6, 7} [0, 0, 0, 0, 0, 1, 3, 1] {1, 2, 6, 7} [0, 0, 0, 0, 17, 27, 10, 1] {2, 6, 7} [0, 0, 0, 0, 10, 27, 12, 1] {1, 6, 7} [0, 0, 0, 179, 259, 127, 23, 1] {6, 7} [0, 0, 0, 0, 0, 0, 0, 1] {1, 2, 3, 4, 5, 7} [0, 0, 0, 0, 0, 0, 4, 2] {2, 3, 4, 5, 7} [0, 0, 0, 0, 0, 0, 3, 2] {1, 3, 4, 5, 7} [0, 0, 0, 0, 0, 12, 16, 3] {3, 4, 5, 7} [0, 0, 0, 0, 0, 0, 2, 3] {1, 2, 4, 5, 7} [0, 0, 0, 0, 0, 17, 15, 2] {2, 4, 5, 7} [0, 0, 0, 0, 0, 2, 11, 2] {1, 4, 5, 7} [0, 0, 0, 0, 30, 77, 32, 3] {4, 5, 7} [0, 0, 0, 0, 0, 0, 0, 1] {1, 2, 3, 5, 7} [0, 0, 0, 0, 0, 0, 4, 3] {2, 3, 5, 7} [0, 0, 0, 0, 0, 1, 5, 1] {1, 3, 5, 7} [0, 0, 0, 0, 2, 35, 21, 2] {3, 5, 7} [0, 0, 0, 0, 0, 0, 2, 1] {1, 2, 5, 7} [0, 0, 0, 0, 0, 21, 14, 1] {2, 5, 7} [0, 0, 0, 0, 2, 22, 11, 1] {1, 5, 7} [0, 0, 0, 70, 214, 140, 26, 1] {5, 7} [0, 0, 0, 0, 0, 0, 2, 1] {1, 2, 3, 4, 7} [0, 0, 0, 0, 0, 8, 12, 1] {2, 3, 4, 7} [0, 0, 0, 0, 0, 5, 8, 1] {1, 3, 4, 7} [0, 0, 0, 0, 28, 67, 28, 3] {3, 4, 7} [0, 0, 0, 0, 0, 2, 7, 1] {1, 2, 4, 7} [0, 0, 0, 0, 24, 43, 14, 1] {2, 4, 7} [0, 0, 0, 0, 2, 27, 17, 2] {1, 4, 7} [0, 0, 0, 76, 266, 208, 58, 5] {4, 7} [0, 0, 0, 0, 0, 2, 7, 1] {1, 2, 3, 7} [0, 0, 0, 0, 9, 28, 15, 1] {2, 3, 7} [0, 0, 0, 0, 9, 28, 10, 1] {1, 3, 7} [0, 0, 0, 56, 198, 132, 26, 1] {3, 7} [0, 0, 0, 0, 3, 14, 8, 1] {1, 2, 7} [0, 0, 0, 50, 139, 86, 16, 1] {2, 7} [0, 0, 0, 22, 125, 92, 21, 1] {1, 7} [0, 0, 746, 1512, 1089, 336, 40, 1] {7} [0, 0, 0, 0, 0, 0, 0, 1] {1, 2, 3, 4, 5, 6} [0, 0, 0, 0, 0, 0, 5, 1] {2, 3, 4, 5, 6} [0, 0, 0, 0, 0, 0, 8, 3] {1, 3, 4, 5, 6} [0, 0, 0, 0, 0, 31, 20, 3] {3, 4, 5, 6} [0, 0, 0, 0, 0, 0, 4, 2] {1, 2, 4, 5, 6} [0, 0, 0, 0, 0, 24, 12, 1] {2, 4, 5, 6} [0, 0, 0, 0, 0, 13, 15, 3] {1, 4, 5, 6} [0, 0, 0, 0, 106, 111, 35, 3] {4, 5, 6} [0, 0, 0, 0, 0, 0, 2, 3] {1, 2, 3, 5, 6} [0, 0, 0, 0, 0, 4, 13, 4] {2, 3, 5, 6} [0, 0, 0, 0, 0, 14, 11, 1] {1, 3, 5, 6} [0, 0, 0, 0, 31, 72, 28, 2] {3, 5, 6} [0, 0, 0, 0, 0, 3, 8, 1] {1, 2, 5, 6} [0, 0, 0, 0, 29, 64, 21, 1] {2, 5, 6} [0, 0, 0, 0, 27, 45, 15, 1] {1, 5, 6} [0, 0, 0, 311, 441, 198, 30, 1] {5, 6} [0, 0, 0, 0, 0, 0, 3, 2] {1, 2, 3, 4, 6} [0, 0, 0, 0, 0, 12, 21, 5] {2, 3, 4, 6} [0, 0, 0, 0, 0, 9, 10, 1] {1, 3, 4, 6} [0, 0, 0, 0, 43, 98, 47, 6] {3, 4, 6} [0, 0, 0, 0, 0, 3, 10, 4] {1, 2, 4, 6} [0, 0, 0, 0, 29, 69, 31, 2] {2, 4, 6} [0, 0, 0, 0, 6, 32, 21, 2] {1, 4, 6} [0, 0, 0, 92, 342, 269, 69, 5] {4, 6} [0, 0, 0, 0, 0, 3, 8, 1] {1, 2, 3, 6} [0, 0, 0, 0, 9, 35, 22, 2] {2, 3, 6} [0, 0, 0, 0, 21, 35, 11, 1] {1, 3, 6} [0, 0, 0, 84, 267, 177, 33, 1] {3, 6} [0, 0, 0, 0, 4, 20, 12, 1] {1, 2, 6} [0, 0, 0, 62, 199, 125, 21, 1] {2, 6} [0, 0, 0, 50, 178, 119, 23, 1] {1, 6} [0, 0, 1026, 2032, 1405, 399, 42, 1] {6} [0, 0, 0, 0, 0, 0, 4, 1] {1, 2, 3, 4, 5} [0, 0, 0, 0, 0, 20, 12, 1] {2, 3, 4, 5} [0, 0, 0, 0, 0, 22, 13, 1] {1, 3, 4, 5} [0, 0, 0, 0, 120, 126, 38, 3] {3, 4, 5} [0, 0, 0, 0, 0, 14, 16, 3] {1, 2, 4, 5} [0, 0, 0, 0, 92, 90, 23, 1] {2, 4, 5} [0, 0, 0, 0, 49, 89, 41, 5] {1, 4, 5} [0, 0, 0, 472, 775, 442, 100, 7] {4, 5} [0, 0, 0, 0, 0, 5, 9, 2] {1, 2, 3, 5} [0, 0, 0, 0, 10, 43, 39, 7] {2, 3, 5} [0, 0, 0, 0, 27, 43, 14, 1] {1, 3, 5} [0, 0, 0, 72, 319, 270, 73, 5] {3, 5} [0, 0, 0, 0, 9, 25, 15, 1] {1, 2, 5} [0, 0, 0, 88, 265, 187, 37, 1] {2, 5} [0, 0, 0, 79, 202, 129, 25, 1] {1, 5} [0, 0, 1208, 2496, 1864, 600, 75, 2] {5} [0, 0, 0, 0, 0, 17, 10, 1] {1, 2, 3, 4} [0, 0, 0, 0, 93, 98, 25, 1] {2, 3, 4} [0, 0, 0, 0, 66, 60, 14, 1] {1, 3, 4} [0, 0, 0, 420, 656, 346, 70, 4] {3, 4} [0, 0, 0, 0, 38, 58, 21, 1] {1, 2, 4} [0, 0, 0, 308, 435, 195, 29, 1] {2, 4} [0, 0, 0, 90, 242, 174, 42, 3] {1, 4} [0, 0, 1377, 2987, 2427, 910, 154, 9] {4} [0, 0, 0, 0, 36, 50, 15, 1] {1, 2, 3} [0, 0, 0, 121, 270, 180, 37, 1] {2, 3} [0, 0, 0, 191, 248, 105, 18, 1] {1, 3} [0, 0, 1120, 2261, 1621, 486, 53, 1] {3} [0, 0, 0, 68, 149, 87, 16, 1] {1, 2} [0, 0, 857, 1612, 1040, 269, 26, 1] {2} [0, 0, 750, 1455, 994, 290, 34, 1] {1} [4160, 14560, 20202, 14105, 5180, 945, 70, 1] {} 2 3 4 5 6 7 4160 + 14560 q + 27286 q + 31421 q + 22880 q + 10144 q + 2422 q + 227 q