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# Tessellations

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by

## Stephanie Wall

on 4 April 2013

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#### Transcript of Tessellations

Tessellations A tessellation is the repeated use of shapes to fill a flat surface with out gaps or overlaps. What is a tessellation? Tessellations can be found throughout art history; from ancient art to modern art. Tessellations can even be found in nature. HONEYCOMB There are different types of tessellations, for example, regular and semi-regular tessellations. Regular tessellations only use
one type of shape. Semi-regular tessellations use different types of shapes. There are only 3 regular tessellations that exist, equilateral triangles, squares and hexagons. Semi-regular tessellations (or Archimedean tessellations) have two properties:

They are formed by two or more types of regular polygon

Each vertex has the same pattern of polygons around it. One rule of tessellation is that the sides NEVER overlap! No tile shares a partial side with any other tile. à Tessellations are created by using transformations. Remember that transformations is how we change the position of a shape. Translations: when a shape is moved in any direction. Reflections: A mirror image that is made of the original shape. Rotations: The original shape is rotated around a central point. Glide reflections: The figure that results after reflection and translation. Tessellations are also used in computer graphics. They are used in 3-D Animation! Tessellations are even used in video games to make everything look more realistic. They work by breaking down polygons into smaller, finer pieces. When a displacement map is applied to a surface, it allows the vertices on that certain surface to be shifted up or down based on the height information. Another popular technique is applying displacement maps over the world in the game so the game makers can carve out craters, canyons and mountains in the landscape. Some games like skyrim and assassins creed already show off the amazing potential that tessellations have. NOW IT'S YOUR TURN. CREATE A WORK OF ART USING POLYGONS THAT TESSELLATE. THE END TURTLE PINEAPPLE Remember the rules:
1. NO GAPS!
2. NO OVERLAPPING!
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