1. The number of equilateral triangles that can be formed by three vertices of a cube is
(A) 4;
(B) 8 ;
(C) 12;
(D) 24.
1. (B)

At a vertex of a cube, there are three mutually perpendicular faces, on each of which a diagonal is drawn, and these diagonals together form a unique equilateral triangle. This establishes a one-to-one correspondence between the equilateral triangles and the vertices, and since a cube has 8 vertices, there are exactly 8 equilateral triangles.