D5

# Dynkin diagram
 
       2
       |
   1---3---4---5
 
# coordinates (and numbering of) the positive co-roots

1   [1, 0, 0, 0, 0]
2   [0, 1, 0, 0, 0]
3   [0, 0, 1, 0, 0]
4   [0, 0, 0, 1, 0]
5   [0, 0, 0, 0, 1]
6   [1, 0, 1, 0, 0]
7   [0, 1, 1, 0, 0]
8   [0, 0, 1, 1, 0]
9   [0, 0, 0, 1, 1]
10   [1, 1, 1, 0, 0]
11   [1, 0, 1, 1, 0]
12   [0, 1, 1, 1, 0]
13   [0, 0, 1, 1, 1]
14   [1, 1, 1, 1, 0]
15   [1, 0, 1, 1, 1]
16   [0, 1, 1, 1, 1]
17   [1, 1, 2, 1, 0]
18   [1, 1, 1, 1, 1]
19   [1, 1, 2, 1, 1]
20   [1, 1, 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, 0]   {1, 3, 4, 5}
[0, 0, 0, 0, 2]   {3, 4, 5}
[0, 0, 0, 0, 1]   {1, 4, 5}
[0, 0, 0, 5, 1]   {4, 5}
[0, 0, 0, 0, 1]   {1, 3, 5}
[0, 0, 0, 4, 2]   {3, 5}
[0, 0, 0, 1, 1]   {1, 5}
[0, 0, 14, 10, 1]   {5}
[0, 0, 0, 0, 1]   {1, 3, 4}
[0, 0, 0, 9, 3]   {3, 4}
[0, 0, 0, 2, 1]   {1, 4}
[0, 0, 19, 12, 1]   {4}
[0, 0, 0, 3, 1]   {1, 3}
[0, 0, 22, 17, 3]   {3}
[0, 0, 10, 8, 1]   {1}
[70, 140, 90, 20, 1]   {}
                                        2       3       4
                      70 + 140 q + 155 q  + 91 q  + 21 q