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A cube (or hexahedron) is a Platonic solid composed of six square faces, with three meeting at each vertex. The cube is a special kind of square prism and of triangular trapezohedron[?], and is dual to the octahedron. Canonical coordinates for the vertices of a cube centered at the origin are (±1,±1,±1), while the interior of the same consists of all points (x0, x1, x2) with -1 < xi < 1.

A cube can be inscribed in a dodecahedron so that each vertex of the cube is a vertex of the dodecahedron and each edge is a diagonal of one of the dodecahedron's faces; taking all such cubes gives rise to the regular compound of five cubes. The compound of two tetrahedra is made from the cube in like fashion. The cube is unique among the Platonic solids for being able to tile space regularly, and finds many uses because of this. For instance, sugar is usually cut into cubes. The familiar six-sided die is also cube shaped.

In arithmetics and algebra, the cube of an entity x is the result of multiplying it with itself two times. This is the same as computing the volume of a geometric cube of size x, and the same as x raised to the power of three: x3 = x × x × x.

The opposite operation of finding the real number that, multiplied with itself two times, becomes x is called the cube root[?] of x. This is the same as x raised to the power of one-third.

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