The 16 points above lie in a plane on an equilateral triangular lattice.

Certain sets of three points of the figure correspond to the vertices of equilateral triangles.

Suppose you were to form all of the equilateral triangles possible, such that, for any given

equilateral triangle, it must have its three vertices coincide with three of the 16 points.

### How many total equilateral triangles can be formed this way in the figure?