tessellate, tessalation, crystallographer

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Miyahata Jōmon Museum's Faceted Ceiling

The tessellated geometry is both complex and structural, echoing the exposed excavated ruins in the entrance while providing support to the roof above.

ARCHITECTMAGAZINE.COM

A tessellated plane seen in street pavement.A tessellation or tiling of the plane is a collection of plane figures that fills the plane with no overlaps and no gaps. One may also speak of tessellations of the parts of the plane or of other surfaces. Generalizations to higher dimensions are also possible. Tessellations frequently appeared in the art of M.C. Escher. Tessellations are seen throughout art history, from ancient architecture to modern art.
In Latin, tessella was a small cubical piece of clay, stone or glass used to make mosaics. The word "tessella" means "small square" (from "tessera", square, which in its turn is from the Greek word for "four"). It corresponds with the everyday term tiling which refers to applications of tessellation, often made of glazed clay.


Spotlight

Escher's 'Hand With Globe'
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Graphic artist M.C. Escher was born on this date in 1898. In his work, Escher repeatedly asked the question, "Are you really sure that a floor can't also be a ceiling?" His drawings tease the brain, twisting out and around and back in on themselves until the viewer can no longer distinguish top from bottom or whether the stairs lead up or down. They are proof that what you see is definitely not always what you get. Though he was not formally trained in math or science, mathematicians and scientists (especially crystallographers) have studied Escher's works as fine examples of spatial illusions and tessalations.

Quote

"Only those who attempt the absurd will achieve the impossible. I think it's in my basement... let me go upstairs and check." — M.C. Escher

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A tessellation is a repeating pattern of polygons that covers a plane with no gaps or overlaps. What kind of tessellations can you make out of regular polygons?密鋪（Tessellation）或稱平面填充、細分曲面（subdivision surface），是指把一些較小的表面填滿一個較大的表面而不留任何空隙。在數學上，密鋪可以推廣到更高的維度，稱為空間填充。

有規律的密鋪具有周期性的重覆模式，較特殊的種類有平面正密鋪由正多邊形組成，而且是由同一種形狀獨立完成整個密鋪，和平面半正密鋪與擬半正密鋪用不只一個正多邊形完成密鋪，前者在每個角落都有相同配置，後者則是周期性的重覆模式。有規律的密鋪形成的圖案可分為17組。缺乏重複圖案的密鋪被稱為「非週期密鋪」。非週期性平鋪使用一些較小的表面填滿一個較大的表面而不留任何空隙，但由於每一片的形狀皆不相同，以致無法形成重複圖案。

目錄

  [隱藏] 
• 1在幾何學中
• 2在電腦圖形中
• 3例子
• 4參見
• 5參考資料
• 6外部連結

Tessellation Creator - Illuminations

tessellate

(tĕs'ə-lāt') tr.v., -lat·ed, -lat·ing, -lates.
To form into a mosaic pattern, as by using small squares of stone or glass.

[From Latin tessellātus, of small square stones, from tessella, small cube, diminutive of tessera, a square. See tessera.]

v. tr. - 把...鑲裝花紋

v. - 切りばめ細工にする, 互いにぴったり合う
adj. - モザイクの, 格子模様のある

tessellation tes'sel·la'tion n. tessellation