Erdos distance problem n=12

Here goes my poor explanation:

Take a regular hexagonal lattice with distance 1 between nearest neighbors, and choose a 15-point equilateral triangle in this lattice (15 is a triangular number). Remove the 3 vertices of the triangle. You'll be left with 12 points and 5 distinct distances.

Edit: Just checked the OEIS reference, and it's available on Google Books. The picture you want is on page 200.

If I may supplement Logan Maingi's apposite answer with a snapshot of the page to which he refers:

(I couldn't resist including the surrounding conjecture.)

Thought it might be nice to show the set placed on the hexagonal lattice.

Here’s a Desmos link if you wish to play around with such point configurations.