12. (12 points) The figure below shows a triangular array of 15 points. To ensure that no equilateral triangles remain with the points in the figure as vertices, at least ( ) points must be removed.
A. 6
B. 7
C. 8
D. 9
【Solution】Solution: Let the side length of the smallest equilateral triangle be 1. As shown in Figure 1, with $A$ as the vertex, equilateral triangles with side lengths of 4, 3, 2, and 1 can be formed, so point $A$ must be removed. Similarly, points $B$ and $C$ must also be removed.

As shown in Figure 2 (blanks indicate points that must be removed), four equilateral triangles with side lengths of 2 and several equilateral triangles with side lengths of 1 are formed, so points $O$, $D$, $E$, and $F$ must be removed.

Therefore, a total of 7 points have been removed.
Hence, the answer is: $B$.