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 tiling.

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 x x4o.

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 x x.