Techniques
Treating tessellations as grids is a method of creating new tessellations.
To use grids to make tessellations, you can do any of the following:
- Superimpose (overlap) two copies of the same tessellation.
- Rotate a copy of a tessellation and then superimpose it on the
original.
- Superimpose two different tessellations.
- Rotate each individual shape of a tessellation.
Here are examples of the first technique (overlap two copies of
the same tessellation).
in black: the 3.3.3.3.3.3 regular tessellation; in red: a copy
of the original tessellation
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The resulting tessellation
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in black: the 3.3.3.3.3.3 / 3.3.4.12 demiregular tessellation;
in red: a copy of the original tessellation
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The resulting tessellation
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Here is an example of the second technique (rotation of the original
tessellation).
in black: a tessellation of squares; in red: a copy of the original
tessellation, rotated 37 degrees
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The resulting tessellation
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Here is an example of the third technique (overlap of two different
tessellations). A grid of equilateral triangles is placed on top
of a grid of squares; the triangles and squares have the same
side lengths.
in black: a tessellation of rectangles; in red: the 3.3.3.3.3.3
regular tessellation (equilateral triangles)
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The resulting tessellation
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Here is an example of the fourth technique (rotation of individual
shapes). Each polygon of an existing tiling has been rotated by
45 degrees.
in black: the 3.4.6.4 semiregular tessellation; in red: each polygon
has been rotated 45 degrees around its center
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The resulting tessellation
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 Additionally, after having done the hands-on activity, you may
want to print two or more copies of a regular, semiregular, or
demiregular tessellation onto transparency paper. This way, you
can experiment overlapping two copies of the same tessellation
and easily see what results. Click on the icon to the right to
proceed to the templates page.
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