E6 # Dynkin diagram 2 | 1---3---4---5---6 # coordinates (and numbering of) the positive co-roots 1 [1, 0, 0, 0, 0, 0] 2 [0, 1, 0, 0, 0, 0] 3 [0, 0, 1, 0, 0, 0] 4 [0, 0, 0, 1, 0, 0] 5 [0, 0, 0, 0, 1, 0] 6 [0, 0, 0, 0, 0, 1] 7 [1, 0, 1, 0, 0, 0] 8 [0, 1, 0, 1, 0, 0] 9 [0, 0, 1, 1, 0, 0] 10 [0, 0, 0, 1, 1, 0] 11 [0, 0, 0, 0, 1, 1] 12 [1, 0, 1, 1, 0, 0] 13 [0, 1, 1, 1, 0, 0] 14 [0, 1, 0, 1, 1, 0] 15 [0, 0, 1, 1, 1, 0] 16 [0, 0, 0, 1, 1, 1] 17 [1, 1, 1, 1, 0, 0] 18 [1, 0, 1, 1, 1, 0] 19 [0, 1, 1, 1, 1, 0] 20 [0, 1, 0, 1, 1, 1] 21 [0, 0, 1, 1, 1, 1] 22 [1, 1, 1, 1, 1, 0] 23 [1, 0, 1, 1, 1, 1] 24 [0, 1, 1, 2, 1, 0] 25 [0, 1, 1, 1, 1, 1] 26 [1, 1, 1, 2, 1, 0] 27 [1, 1, 1, 1, 1, 1] 28 [0, 1, 1, 2, 1, 1] 29 [1, 1, 2, 2, 1, 0] 30 [1, 1, 1, 2, 1, 1] 31 [0, 1, 1, 2, 2, 1] 32 [1, 1, 2, 2, 1, 1] 33 [1, 1, 1, 2, 2, 1] 34 [1, 1, 2, 2, 2, 1] 35 [1, 1, 2, 3, 2, 1] 36 [1, 2, 2, 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] {1, 2, 3, 4} [0, 0, 0, 0, 2] {2, 3, 4} [0, 0, 0, 0, 1] {1, 3, 4} [0, 0, 0, 8, 3] {3, 4} [0, 0, 0, 0, 2] {1, 2, 4} [0, 0, 0, 11, 4] {2, 4} [0, 0, 0, 3, 2] {1, 4} [0, 0, 34, 30, 6] {4} [0, 0, 0, 0, 1] {1, 2, 3} [0, 0, 0, 4, 3] {2, 3} [0, 0, 0, 4, 1] {1, 3} [0, 0, 26, 18, 2] {3} [0, 0, 0, 2, 1] {1, 2} [0, 0, 22, 15, 1] {2} [0, 0, 17, 10, 1] {1} [105, 210, 133, 28, 1] {} 2 3 4 105 + 210 q + 232 q + 133 q + 31 q