Cube
A cube is a three-dimensional solid object in geometry. It 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. It is a special case of a cuboid, a parallelepiped, and a rhombohedron in which all six quadrilateral faces are squares. It is a three-dimensional hypercube, a family of polytopes that also includes the two-dimensional square and four-dimensional tesseract.
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 can be represented in many ways. One of them is by drawing a graph with vertices connected with an edge in a plane. Such a graph is called the cubical graph, a special case of the hypercube graph.
The cube is the core of many polyhedra's construction or other geometrical shapes. For example, truncating a cube's vertices results in a truncated cube. Joining one or more cubes face-to-face yields a polycube, a three-dimensional version of polyominoes. Two or more cubes can have the same centre, forming polyhedral compounds. Cubes can form a honeycomb by attaching face-to-face, filling a space without leaving a gap.
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