3
1 5
5 4 4
5 3 5 5
5 5 3 2 1
1 0 0 5 5 5
1 5 5 4 2 2 0
3
4 3
1 1 4
0 4 4 4
4 4 3 2 4
2 0 0 4 2 1
0
3 1
2 1 3
0 3 3 2
3 0 3 3 2
2
2 2
1 2 0
2 1 0 2
1
1 1
1 0 0
0
0 0
There are 56 Tetrominoes in a set; one for each combination of three numbers between 0 and 5. The pieces with distinct numbers always have them arranged ascending clockwise.
If you group the pieces by their maximum number, they fall into groups of size 1, 3, 6, 10, 15, and 21. Each group can be arranged in a triangle if its pieces are all oriented alike. And it turns out, as shown above, that this can be done in such a way that adjacent corners match.