Example 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
Now, consider a vertex with three mutually perpendicular faces, each having 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. Since a cube has 8 vertices, there are exactly 8 equilateral triangles.