Cube

A cube is a three-dimensional solid object in geometry. A cube has eight vertices and twelve straight edges of the same length, so that these edges form six square faces of the same size. It is an example of a polyhedron. The cube is found in many popular cultures, including toys and games, the arts, optical illusions, and architectural buildings. Cubes can be found in crystal structures, science, and technological devices. It is also found in ancient texts, such as Plato's work Timaeus, which described a set of solids now called Platonic solids, associating a cube with the classical element of earth. A cube with unit length is the canonical unit of volume in three-dimensional space, relative to which other solid objects are measured. The cube relates to the construction of many polyhedra, such as truncation and attaching to other polyhedra. It also represents geometrical shapes. The cube can be attached to its faces with its copy to fill a space without leaving a gap, which forms a honeycomb. The cube can be represented in many ways. One example is by drawing a graph, a structure in graph theory consisting of a set of vertices that are connected with an edge. This graph also represents the family of a cuboid, a polyhedron with six quadrilateral faces, which includes the cube as its special case. The cube and its graph are a three-dimensional hypercube, a family of polytopes that also includes the two-dimensional square and four-dimensional tesseract.