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Employing a solid cover or grating that is flush with the surrounding surface, this drain is commonly made of concrete in-situ and with the option of using polymer- or metal-based liners or a channel former to aid in channel crafting and slope formation. The drain is characterized by its long length and narrow width, the cross-section of the ...
In geometry, a tiling is a partition of the plane (or any other geometric setting) into closed sets (called tiles), without gaps or overlaps (other than the boundaries of the tiles). [1] A tiling is considered periodic if there exist translations in two independent directions which map the tiling onto itself.
These shapes are called prototiles, and a set of prototiles is said to admit a tiling or tile the plane if there is a tiling of the plane using only these shapes. That is, each tile in the tiling must be congruent to one of these prototiles. [4] A tiling that has no periods is non-periodic.
The phrase "tile drainage" derives from its original composition from ceramic tiles of fired clay, which were similar to terracotta pipes yet not always shaped as pipes. In the 19th century a C-shaped channel tile commonly was placed like an arch atop a flat tile, denominated the "mug" and "sole", respectively.
Subsurface drains, on the other hand, are designed to manage water that seeps into the soil beneath the planting surface. French drains, which are gravel-filled trenches with perforated pipes at the bottom, are the most common type of subsurface drain. Trench drains, which are similar but shallower and wider, are also used in some situations. [4]
The Socolar–Taylor tile was proposed in 2010 as a solution to the einstein problem, but this tile is not a connected set. In 1996, Petra Gummelt constructed a decorated decagonal tile and showed that when two kinds of overlaps between pairs of tiles are allowed, the tiles can cover the plane, but only non-periodically. [6]
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