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Hexagonal tiling is the densest way to arrange circles in two dimensions. The honeycomb conjecture states that hexagonal tiling is the best way to divide a surface into regions of equal area with the least total perimeter.
A tiling that cannot be constructed from a single primitive cell is called nonperiodic. If a given set of tiles allows only nonperiodic tilings, then this set of tiles is called aperiodic. [3] The tilings obtained from an aperiodic set of tiles are often called aperiodic tilings, though strictly speaking it is the tiles themselves that are ...
Mesh is a measurement of particle size often used in determining the particle-size distribution of a granular material. For example, a sample from a truckload of peanuts may be placed atop a mesh with 5 mm openings. When the mesh is shaken, small broken pieces and dust pass through the mesh while whole peanuts are retained on the mesh.
A cement board is a combination of cement and reinforcing fibers formed into sheets, of varying thickness that are typically used as a tile backing board. [1] Cement board can be nailed or screwed to wood or steel studs to create a substrate for vertical tile and attached horizontally to plywood for tile floors, kitchen counters and backsplashes.
The elaborate and colourful zellige tessellations of glazed tiles at the Alhambra in Spain that attracted the attention of M. C. Escher. More formally, a tessellation or tiling is a cover of the Euclidean plane by a countable number of closed sets, called tiles, such that the tiles intersect only on their boundaries. These tiles may be polygons ...
The matching rules force a particular substitution: the two A L tiles in a φ A L tile must form a kite, and thus a kite decomposes into two kites and a two half-darts, and a dart decomposes into a kite and two half-darts. [45] [46] Enlarged φ B-tiles decompose into B-tiles in a similar way (via φ A-tiles).