In mathematics, tessellation can be generalized to higher dimensions and a variety of geometries.Ī periodic tiling has a repeating pattern. Rev.An example of non‑periodicity due to another orientation of one tile out of an infinite number of identical tiles.Ī tessellation or tiling is the covering of a surface, often a plane, using one or more geometric shapes, called tiles, with no overlaps and no gaps. Stephenson, J.: Ising model with antiferromagnetic next-nearest-neighbor coupling: spin correlations and disorder points. Radványi, A.G.: On the rectangular grid representation of general CNN networks. Räbinä, J., Kettunen, L., Mönkölä, S., Rossi, T.: Generalized wave propagation problems and discrete exterior calculus.

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Kovács, G., Nagy, B., Vizvári, B.: On weighted distances on the Khalimsky grid. Kovács, G., Nagy, B., Turgay, N.D.: Distance on the Cairo pattern. Kirby, M., Umble, R.: Edge tessellations and stamp folding puzzles. Her, I.: Geometric transformations on the hexagonal grid. Her, I.: A symmetrical coordinate frame on the hexagonal grid for computer graphics and vision. Grünbaum, B., Shephard, G.C.: Tilings by regular polygons.

Keywordsīorgefors, G.: A semiregular image grid. Moreover, we are also presenting formulae to compute the digital, i.e., path-based distance based on the length of a/the shortest path(s) through neighbor tiles for these specific grids. For some of those grids, including the tetrille tiling D(6, 4, 3, 4) (also called deltoidal trihexagonal tiling and it is the dual of the rhombihexadeltille, T(6, 4, 3, 4) tiling), the rhombille tiling, D(6, 3, 6, 3) (that is the dual of the hexadeltille T(6, 3, 6, 3), also known as trihexagonal tiling) and the kisquadrille tiling D(8, 8, 4) (it is also called tetrakis square tiling and it is the dual of the truncated quadrille tiling T(8, 8, 4) which is also known as Khalimsky grid) we give detailed descriptions. The properties of the coordinate systems used to address the tiles are playing crucial roles. We show a general method to obtain coordinate system to address the tiles of these tessellations. In this paper, we are interested to their dual tessellations. There are eight semi-regular tessellations, they are based on more than one type of tiles. The square grid is self-dual, and the two others, the hexagonal and triangular grids are duals of each other. There are three regular ones, each of them using a sole regular tile. There are various tessellations of the plane.

Semi regular tessellation in nature