It has been suggested that Sum of two cubes be merged into this article. ( Discuss) Proposed since November 2023.

As the volume of a cube is the third power of its sides a × a × a {\displaystyle a\times a\times a} , third powers are called cubes, by analogy with squares and second powers. In geometry, a cube [a] is a three-dimensional solid object bounded by six square faces, facets, or sides, with three meeting at each vertex. Viewed from a corner, it is a hexagon and its net is usually depicted as a cross. [1] A cube can also be considered the limiting case of a 3D superellipsoid as all three exponents approach infinity.In analytic geometry, a cube's surface with center ( x 0, y 0, z 0) and edge length of 2a is the locus of all points ( x, y, z) such that The cube can also be represented as a spherical tiling, and projected onto the plane via a stereographic projection. This projection is conformal, preserving angles but not areas or lengths. Straight lines on the sphere are projected as circular arcs on the plane. The cube is the only regular hexahedron and is one of the five Platonic solids. It has 6 faces, 12 edges, and 8 vertices.

A cube has the largest volume among cuboids (rectangular boxes) with a given surface area. Also, a cube has the largest volume among cuboids with the same total linear size (length+width+height).The cube is also a square parallelepiped, an equilateral cuboid, a right rhombohedron, and a 3- zonohedron. It is a regular square prism in three orientations, and a trigonal trapezohedron in four orientations. This configuration matrix represents the cube. The rows and columns correspond to vertices, edges, and faces. The diagonal numbers say how many of each element occur in the whole cube. The nondiagonal numbers say how many of the column's element occur in or at the row's element. [2] For example, the 2 in the first column of the middle row indicates that there are 2 vertices in (i.e., at the extremes of) each edge; the 3 in the middle column of the first row indicates that 3 edges meet at each vertex. The cube has four special orthogonal projections, centered, on a vertex, edges, face and normal to its vertex figure. The first and third correspond to the A 2 and B 2 Coxeter planes. displaystyle {\begin{bmatrix}{\begin{matrix}8&3&3\\2&12&2\\4&4&6\end{matrix}}\end{bmatrix}}} Equation in three dimensional space [ edit ] The cube is dual to the octahedron. It has cubical or octahedral symmetry, and is the only convex polyhedron whose faces are all squares. Its generalization for higher-dimensional spaces is called a hypercube.