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Tessellations
Coverings of the plane, or tessellations, using congruent figures has interested artists, artisans, and geometers alike. Many cultures have used tessellations as decorations for houses, temples, and palaces. Use of tiling designs dates back at least as far as the Sumerians in 4000 BCE. One of the most famous examples of the use of tessellations is the Alhambra palace in Granada, Spain, an Islamic masterpiece. Islam forbids the representation of living beings in artwork, thus providing the impetus for some astonishing works of geometric art. A regular tessellation consists of only one type of regular polygon. Semi-regular tessellations use a mix of regular polygons, with the same polygons used in the same order at each vertex.  |
Regular Tessellations
A regular tessellation
consists of only one type of regular
polygon. There are only 3 regular polygons which will tile
the plane
using solely copies of themselves: equilateral triangles, squares, and
regular triangles.
Semi- Regular Tessellations There are exactly 8 ways to tile the plane using two or more regular polygons which meet in an arrangement with identical vertices. The patterns are designated with a sequence of integers which describe the number of sides of each polygon in the order they are arranged around each vertex. The pattern to the right is a 6.3.3.3.3. The eight possibilities are: •
12.12.3
See all of these patterns in the Naked Geometry Book.• 12.6.4 • 8.8.4 • 6.3.6.3 • 6.4.3.4 • 6.3.3.3.3 • 4.4.3.3.3 • 4.3.4.3.3 |
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