$23 \cdot 18$ The number of equilateral triangles formed by three vertices of a cube is
(A) 4.
(B) 8.
(C) 12.
(D) 24.
(China High School Mathematics League, 1991)
［Solution］There are three faces, each having a common vertex and being mutually perpendicular to each other, on which there is a diagonal that together forms a unique equilateral triangle.
Therefore, a one-to-one correspondence can be established between the set of equilateral triangles and the set of vertices.
A cube has a total of 8 vertices, so there are exactly 8 equilateral triangles.
Hence, the answer is $(B)$.