F4 # Dynkin diagram 1---2=<=3---4 # coordinates (and numbering of) the positive co-roots 1 [1, 0, 0, 0] 2 [0, 1, 0, 0] 3 [0, 0, 1, 0] 4 [0, 0, 0, 1] 5 [1, 1, 0, 0] 6 [0, 1, 2, 0] 7 [0, 1, 1, 0] 8 [0, 0, 1, 1] 9 [1, 1, 2, 0] 10 [0, 1, 2, 2] 11 [1, 1, 1, 0] 12 [0, 1, 1, 1] 13 [1, 2, 2, 0] 14 [1, 1, 2, 2] 15 [1, 1, 1, 1] 16 [0, 1, 2, 1] 17 [1, 2, 2, 2] 18 [1, 1, 2, 1] 19 [1, 2, 4, 2] 20 [1, 2, 2, 1] 21 [1, 3, 4, 2] 22 [1, 2, 3, 1] 23 [2, 3, 4, 2] 24 [1, 2, 3, 2] # 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, 1] {2, 3, 4} [0, 0, 0, 0, 1] {1, 3, 4} [0, 0, 0, 4, 1] {3, 4} [0, 0, 0, 0, 2] {1, 2, 4} [0, 0, 0, 3, 2] {2, 4} [0, 0, 0, 2, 1] {1, 4} [0, 0, 17, 10, 1] {4} [0, 0, 0, 0, 2] {1, 2, 3} [0, 0, 0, 8, 3] {2, 3} [0, 0, 0, 4, 3] {1, 3} [0, 0, 26, 18, 2] {3} [0, 0, 0, 11, 4] {1, 2} [0, 0, 34, 30, 6] {2} [0, 0, 22, 15, 1] {1} [105, 210, 133, 28, 1] {} 2 3 4 105 + 210 q + 232 q + 133 q + 31 q