Cube

This article is about the geometric shape. For other meanings of the word "cube", see cube (disambiguation).

A cube English cube from Old French < Latin cubus < Greek kubos, "a cube, a die, vertebra". In turn from PIE *keu(b)-, "to bend, turn". (or regular hexahedron) is a three-dimensional Platonic solid composed of six square faces, facets or sides, with three meeting at each vertex. The cube is a special kind of square prism, of rectangular parallelepiped and of 3-sided trapezohedron, and is dual to the octahedron. Thus it has octahedral symmetry. A cube is the three-dimensional case of the more general concept of a measure polytope.

Contents

1 Cartesian coordinates
2 Formulas
3 Geometric relations
4 Higher dimensions
5 Related polyhedra
6 Combinatorial cubes
7 Note
8 See also
9 External links

Cartesian coordinates

Cartesian coordinates for the vertices of a cube centered at the origin and edge length 2 are

(±1,±1,±1)

while the interior of the same consists of all points (x₀, x₁, x₂) with -1 < x_i < 1.

Formulas

For a cube of edge length [a],

surface area

[6 a^2]

volume

[a^3]

radius of circumscribed sphere

[\frac

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