A3

# Dynkin diagram
 
   1---2---3
 
# coordinates (and numbering of) the positive co-roots

1   [1, 0, 0]
2   [0, 1, 0]
3   [0, 0, 1]
4   [1, 1, 0]
5   [0, 1, 1]
6   [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, 1]   {1}
[6, 6, 1]   {}
                                              2
                                 6 + 6 q + 3 q