Cube this problem, and in 1837 Pierre Wantzel proved it to be impossible because the cube root of 2 is not a constructible number. The cube has three uniform colorings, named by the colors of the square faces around each vertex: 111, 112, 123. The cube has three classes of symmetry, which can be represented by vertex-transitive coloring the faces. The highest octahedral symmetry O has all the faces the same color. The dihedral symmetry D comes from the cube being a prism, with all four sides being the same color. The lowest symmetry D is also a prismatic symmetry, with
The Cube Root of Uncertainty The Cube Root of Uncertainty The Cube Root of Uncertainty is a collection of science fiction short stories by American writer Robert Silverberg, published in hardcover by Macmillan in 1970 and issued in paperback by Collier Books in 1971. No further editions have been issued. "Passengers" won the Nebula Award for Best Short Story and was nominated for the Hugo Award. Joanna Russ gave the collection a mixed review, noting its division between early work ("Old Silverberg is an idiot") and more recent efforts ("New Silverberg is something else: a highly colored, gloomy, melodramatic, morally allegorical writer who luxuriates in