13. The answer is 4. Up to isometries, it is possible to determine an obtuse triangle, a right triangle, and two different equilateral triangles.

(Busoni)
13. Let $A B C$ be an equilateral triangle, and let $D, E, F$ be the midpoints of the sides. How many non-degenerate and non-congruent triangles can be obtained by choosing 3 of the points $A, B, C, D, E, F$?