Introduction
Division is a technique for making new tilings from existing ones.
In division, some or all of the shapes of a tessellation are divided.
Usually, all similar shapes are divided in the same way so that
the tessellation's regularity is maintained. There are many, many
different ways to divide shapes. Conventional techniques involve
centroids, diagonals, and midpoints.
Centroids
The centroid of a polygon is simply the center of balance for
the polygon. In regular polygons, the centroid is the same distance
from all vertices and is also the same distance from all sides.
Centroids of some regular polygons
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How do we use centroids to divide polygons? One way is to draw
lines from each vertex to the centroid.
One way to divide a polygon is to use draw lines from each vertex
to the centroid
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Here is an example of this division technique involving centroids:
A tessellation of pentagons
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In each pentagon, lines are drawn from each vertex to the centroid
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The original pentagons are removed and the remaining shapes are
colored
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A slight variation of this technique is to draw lines through the centroid to the other end of the polygon instead of just
stopping at the centroid.
Another way to divide a polygon is to draw lines from each vertex
through the centroid to the other side.
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Here is an example of this variation:
The semiregular tessellation 3.3.3.3.6
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In each polygon, lines are drawn from the vertices, through the
centroid, to the other side
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 You may proceed to the templates page to access many ready-made
tessellations on which you can practice the division techniques.
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