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
Cube (algebra) if and only if one can arrange solid unit cubes into a larger, solid cube. For example, 27 small cubes can be arranged into one larger one with the appearance of a Rubik's Cube, since . The difference between the cubes of consecutive integers can be expressed as follows: or There is no minimum perfect cube, since the cube of a negative integer is negative. For example, . Unlike perfect squares, perfect cubes do not have a small number of possibilities for the last two digits. Except for cubes divisible by 5, where only 25, 75 and 00 can be