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)

In a cube, there is a vertex where three faces, each perpendicular to the other two, meet. On these three faces, there are three diagonals that together form a unique equilateral triangle. This establishes a one-to-one correspondence between the equilateral triangles and the vertices. Since a cube has 8 vertices, there are exactly 8 equilateral triangles.