The cube is a special case in various classes of general polyhedra: 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 While the interior consists of all points ( x 0, x 1, x 2) with −1 < x i < 1 for all i.Įquation in three dimensional space Straight lines on the sphere are projected as circular arcs on the plane.įor a cube centered at the origin, with edges parallel to the axes and with an edge length of 2, the Cartesian coordinates of the vertices are This projection is conformal, preserving angles but not areas or lengths. The cube can also be represented as a spherical tiling, and projected onto the plane via a stereographic projection. The first and third correspond to the A 2 and B 2 Coxeter planes. The cube has four special orthogonal projections, centered, on a vertex, edges, face and normal to its vertex figure. The cube is the only convex polyhedron whose faces are all squares. It is a regular square prism in three orientations, and a trigonal trapezohedron in four orientations. The cube is also a square parallelepiped, an equilateral cuboid and a right rhombohedron a 3- zonohedron. It has 6 faces, 12 edges, and 8 vertices. The cube is the only regular hexahedron and is one of the five Platonic solids. Viewed from a corner it is a hexagon and its net is usually depicted as a cross. In geometry, a cube is a three-dimensional solid object bounded by six square faces, facets or sides, with three meeting at each vertex. Regular, convex zonohedron, Hanner polytope For other uses, see Cube (disambiguation).
For cubes in any dimension, see Hypercube. This article is about the 3-dimensional shape.
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