Cube

The cube, or hexahedron, is one of the five Platonic solids. It has 6 square faces, joining 3 to a triangular vertex. It is the 3-dimensional hypercube.

It is the only Platonic solid that can tile 3-dimensional space. This results in the cubic honeycomb.

It is also the uniform square prism.

Vertex coordinates
The vertices of a cube of edge length 1, centered at the origin, are:
 * (±1/2, ±1/2, ±1/2).

Variations
A cube can be considered as the prism product of three mutually orthogonal dyads with the same length. By adjusting the sizes of these edges, we can create variations with different symmetry.

Square prism
A square prism is a variant of the cube constructed as the prism of a square. The two bases are squares, while the 4 lateral sides are rectangles. It can be represented as x4o y. The version with equal edge lengths is a coloring of the cube.

Cuboid
A cuboid, or rectangular prism, is a prism based on a rectangle. It has three different edge types and 6 rectangles as faces, in 3 parallel pairs. It can be represented as x y z. The version with equal edge lengths is a coloring of the cube.

Related polyhedra
The cube can be augmented with a square pyramid to form the elongated square pyramid, a Johnson solid. If the opposite face is also agumented with a square pyramid, the result is the elongated square bipyramid.