1
2 3
4 5 6
7 8 9 a
b c d e f
The only possible points below which a 4-unit triangle can exist are 1 2 3 4 5 6.
The only 4-unit triangle starting, e.g. at 7 is the one covering 7 4 8 2 5 9 which is the same as the one starting at 2.