C3

# 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   [2, 1, 0]
6   [0, 1, 1]
7   [1, 1, 1]
8   [2, 1, 1]
9   [2, 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]   {1, 2, 3}
[0, 0, 0, 2]   {2, 3}
[0, 0, 0, 1]   {1, 3}
[0, 0, 4, 1]   {3}
[0, 0, 0, 1]   {1, 2}
[0, 0, 6, 2]   {2}
[0, 0, 3, 1]   {1}
[20, 30, 12, 1]   {}
                                            2      3
                            20 + 30 q + 25 q  + 9 q