important points on tessellation (in points)
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To tessellate a shape, it must be able to exactly surround a point, or the sum of the angles around each point in a tessellation must be \begin{align*}360^\circ\end{align*}. The only regular polygons with this feature are equilateral triangles, squares, and regular hexagons
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- A tiling or tessellation of a flat surface is the covering of a plane using one or more geometric shapes, called tiles, with no overlaps and no gaps.
- In mathematics, tessellations can be generalized to higher dimensions and a variety of geometries.
- A periodic tiling has a repeating pattern. Some special kinds include regular tilings with regular polygonal tiles all of the same shape, and semiregular tilings with regular tiles of more than one shape and with every corner identically arranged.
- The patterns formed by periodic tilings can be categorized into 17 wallpaper groups.
- A tiling that lacks a repeating pattern is called "non-periodic".
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