0 the process of fitting shapes together in a pattern with no spaces in between, or an arrangement of shapes that has been made in this way: --
Some theories further generalize the idea to include such objects as unbounded polytopes (apeirotopes and tessellations), and abstract polytopes.
A polytope may also be regarded as a tessellation of some given manifold.
The colouring guaranteed by the four-colour theorem will not in general respect the symmetries of the tessellation.
A regular tessellation is a highly symmetric, edge-to-edge tiling made up of regular polygons, all of the same shape.
It is longitudinally crossed by reddish or dark brown stripes, often broken into tessellations on the base.
Equivalently, imagine a tessellation of the plane with regular hexagons, with sides equal to the smallest translation distance divided by 3.
Like for p3, imagine a tessellation of the plane with equilateral triangles of equal size, with the sides corresponding to the smallest translations.
Irregular tessellations can also be made from other shapes such as pentagons, polyominoes and in fact almost any kind of geometric shape.
