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Tessellations of euclidean and hyperbolic space may also be considered regular polytopes. Note that an 'n'-dimensional polytope actually tessellates a space of one dimension less. For example, the (three-dimensional) platonic solids tessellate the 'two'-dimensional 'surface' of the sphere.
In tiling or tessellation problems, there are to be no gaps, nor overlaps. Many of the puzzles of this type involve packing rectangles or polyominoes into a larger rectangle or other square-like shape. There are significant theorems on tiling rectangles (and cuboids) in rectangles (cuboids) with no gaps or overlaps:
Download as PDF; Printable version; In other projects Wikidata item; ... This is a list of tessellations. This list is incomplete; you can help by adding missing items.
Tessellation is used in manufacturing industry to reduce the wastage of material (yield losses) such as sheet metal when cutting out shapes for objects such as car doors or drink cans. [78] Tessellation is apparent in the mudcrack-like cracking of thin films [79] [80] – with a degree of self-organisation being observed using micro and ...
Voronoi tessellations of regular lattices 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 ...
In geometry, many uniform tilings on sphere, euclidean plane, and hyperbolic plane can be made by Wythoff construction within a fundamental triangle, (p q r), defined by internal angles as π/p, π/q, and π/r.