Other
Using centroids, midpoints, and diagonals are common ways that
we can divide polygons. But there are infinitely many other possibilities.
Try inventing some of your own.
Here is some advice:
- Experiment with regular polygons (regular, semiregular, and demiregular
tessellations).
- Use a combination of the midpoint, diagonal, and centroid techniques.
- Try removing the original polygons when you are done.
- Vary the technique from polygon to polygon in a single tessellation.
- Try using a technique only half-way on a polygon. (For example,
choose to draw only every other diagonal.)
- Be sure to repeat modifications throughout the tessellation. (For
example, if you make a little bump in a certain line segment,
be sure to make this same bump on each occurrence of this type
of line segment.)
In the discussion of unit cells (a technique of creating tilings
from scratch), some alternative ways of dividing polygons are
explored. You may want to browse those pages at some point.
  
 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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