A4

# 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, 1, 0]
7   [0, 0, 1, 1]
8   [1, 1, 1, 0]
9   [0, 1, 1, 1]
10   [1, 1, 1, 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]   {1, 2}
[0, 0, 1]   {2}
[0, 0, 2]   {1}
[10, 12, 3]   {}
                                               2
                                10 + 12 q + 6 q