Editing Voronoi diagram (section)

==Examples==
[[Image:Coloured Voronoi 3D slice.svg|right|thumb|This is a slice of the Voronoi diagram of a random set of points in a 3D box. In general, a cross section of a 3D Voronoi tessellation is a [[power diagram]], a weighted form of a 2d Voronoi diagram, rather than being an unweighted Voronoi diagram.]]

Voronoi tessellations of regular [[Lattice (group)|lattice]]s of points in two or three dimensions give rise to many familiar tessellations.
* A 2D lattice gives an irregular honeycomb tessellation, with equal hexagons with point symmetry; in the case of a regular triangular lattice it is regular; in the case of a rectangular lattice the hexagons reduce to rectangles in rows and columns; a [[Square (geometry)|square]] lattice gives the regular tessellation of squares; note that the rectangles and the squares can also be generated by other lattices (for example the lattice defined by the vectors (1,0) and (1/2,1/2) gives squares).
* A [[simple cubic lattice]] gives the [[cubic honeycomb]].
* A [[hexagonal close-packed]] lattice gives a tessellation of space with [[trapezo-rhombic dodecahedron|trapezo-rhombic dodecahedra]].
* A [[face-centred cubic]] lattice gives a tessellation of space with [[rhombic dodecahedron|rhombic dodecahedra]].
* A [[body-centred cubic]] lattice gives a tessellation of space with [[truncated octahedron|truncated octahedra]].
* Parallel planes with regular triangular lattices aligned with each other's centers give the [[hexagonal prismatic honeycomb]].
* Certain body-centered tetragonal lattices give a tessellation of space with [[rhombo-hexagonal dodecahedron|rhombo-hexagonal dodecahedra]].

Certain body-centered tetragonal lattices give a tessellation of space with [[rhombo-hexagonal dodecahedron|rhombo-hexagonal dodecahedra]].

For the set of points (''x'',&nbsp;''y'') with ''x'' in a discrete set ''X'' and ''y'' in a discrete set ''Y'', we get rectangular tiles with the points not necessarily at their centers.