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
Rubik's Cube followed by another 3×2×1 on the opposite side. Next, the corners of the top layer are solved. The cube can then be solved using only moves of the U layer and M slice. Most beginner solution methods involve solving the cube one layer at a time, using algorithms that preserve what has already been solved. The easiest layer by layer methods require only 3–8 algorithms. In 1981, thirteen-year-old Patrick Bossert developed a solution for solving the cube, along with a graphical notation, designed to be easily understood by novices. It was subsequently published as "You Can Do The Cube" and