Cube Cube In geometry, a cube is a three-dimensional solid object bounded by six square faces, facets or sides, with three meeting at each vertex. The cube is the only regular hexahedron and is one of the five Platonic solids. It has 6 faces, 12 edges, and 8 vertices. The cube is also a square parallelepiped, an equilateral cuboid and a right rhombohedron. It is a regular square prism in three orientations, and a trigonal trapezohedron in four orientations. The cube is dual to the octahedron. It has cubical or octahedral symmetry. The cube is the only convex polyhedron whose faces
Principal root of unity Principal root of unity In mathematics, a principal "n"-th root of unity (where "n" is a positive integer) of a ring is an element formula_1 satisfying the equations In an integral domain, every primitive "n"-th root of unity is also a principal formula_3-th root of unity. In any ring, if formula_3 is a power of formula_5, then any formula_6-th root of formula_7 is a principal formula_3-th root of unity. A non-example is formula_9 in the ring of integers modulo formula_10; while formula_11 and thus formula_9 is a cube root of unity, formula_13 meaning that it is not a "principal" cube