Tessellations

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Tessellations
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Tessellations are repeating patterns of distinct
shapes. The word "repeating" means that the
tessellation can be broken down into identical
sections. These sections repeat throughout the
design.
Tessellations are different from patterns in that
patterns usually do not have distinct closed
shapes. A closed shape is a shape that has a
definite interior (inside) and definite exterior
(outside).
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On the left is a true tessellation on the right
is not a tessellation but a pattern. Patterns
repeat but do not have clearly defined closed
shapes. Tessellations repeat and do have clearly
defined closed shapes.
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A pure tessellation consists of congruent copies.
THERE are only three regular polygons that makeup
a pure tessellation! What are they?
Remember Regular means that the sides and angles
of the polygon are all the same length.
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Only three regular polygons tessellate in the
Euclidean plane triangles, squares or hexagons.
Here are examples of
a tessellation of triangles a tessellation of
squares a tessellation of hexagons
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When you look at these three samples you can
easily notice that the squares are lined up with
each other while the triangles and hexagons are
not. Also, if you look at 6 triangles at a time,
they form a hexagon, so the tiling of triangles
and the tiling of hexagons are similar and they
cannot be formed by directly lining shapes up
under each other - a slide (or a glide!) is
involved.
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Examples of Tessellations
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Here are a few sample tessellations created by
famous Dutch artist M. C. Escher