Cube
| Cubical graph | |
|---|---|
 |
|
| Named after | Q3 |
| Vertices | 8 |
| Edges | 12 |
| Radius | 3 |
| Diameter | 3 |
| Girth | 4 |
| Automorphisms | 48 |
| Chromatic number | 2 |
| Properties | Hamiltonian, regular, symmetric, distance-regular, distance-transitive, 3-vertex-connected, planar graph |
In geometry, a cube is a three-dimensional solid object bounded by six square faces, facets or sides, with three meeting at each vertex.
The cube is the only regular hexahedron and is one of the five Platonic solids. It has 6 faces, 12 edges, and 8 vertices.
The cube is also a square parallelepiped, an equilateral cuboid and a right rhombohedron. It is a regular square prism in three orientations, and a trigonal trapezohedron in four orientations.
The cube is dual to the octahedron. It has cubical or octahedral symmetry.
The cube has four special orthogonal projections, centered, on a vertex, edges, face and normal to its vertex figure. The first and third correspond to the A2 and B2Coxeter planes.
The cube can also be represented as a spherical tiling, and projected onto the plane via a stereographic projection. This projection is conformal, preserving angles but not areas or lengths. Straight lines on the sphere are projected as circular arcs on the plane.
For 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
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