(a) In how many distinct ways can we 3-color the edges of a square that is free to move in three dimensions?
(b) In how many distinct ways can we 3-color both the vertices and the edges of such a square?
(c) For a square that can move in three dimensions, let k, m, and n denote the number of distinct ways in which we can 3-color its vertices (alone), its edges (alone), and both its vertices and edges, respectively. Does n = km? (Give a geometric explanation.)