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A Penrose tiling with rhombi exhibiting fivefold symmetry. A Penrose tiling is an example of an aperiodic tiling.Here, a tiling is a covering of the plane by non-overlapping polygons or other shapes, and a tiling is aperiodic if it does not contain arbitrarily large periodic regions or patches.
Delftware wall tiles, typically with a painted design covering only one (rather small) blue and white tile, were ubiquitous in Holland and widely exported over Northern Europe from the 16th century on, replacing many local industries. Several 18th century royal palaces had porcelain rooms with the walls entirely covered in porcelain in tiles or ...
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.
One particular form of the tiling, dual to the snub square tiling, has tiles with the minimum possible perimeter among all pentagonal tilings. Another, overlaying two flattened tilings by regular hexagons, is the form used in Cairo and has the property that every edge is collinear with infinitely many other edges.
An example of a typical NATCO hollow clay tile as advertised in their 1910 catalogue. "The visible points of superiority, as compared with similar tile of different makes, are the deep dovetail scoring for the better bonding of stucco or plaster, the absence of imperfections and the better general symmetry due to the more accurate machining by this company's unequaled equipment.
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