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Geometry 202
9-4 Tessellations
Goal: Identify regular tessellations. Create tessellations with specific attributes.
*Reflections, translations, and rotations can be used to create patterns using polygons.
Think about quilts, soccer balls, pictures, designs… that you have seen before
Defn. A pattern that covers a plane by transforming the same figure or a set of figures so that
there are no overlapping or empty spaces is called a tessellation.
The sum of the angles around any point is 360 degrees.
Easy Tesselations: Investigate Regular Polygons
Squares.
Will these tessellate?
Regular Polygons – Triangle, Square, Pentagon, Hexagon, Heptagon, Octagon
Yes
yes
no
yes
no
no
1) Find the measure of the interior angles.
2) Are they a multiple of 360? If yes, they tessellate. No, they do not.
Ex) Does a regular 16-gon tessellate the plane?
A regular tessellation is a tessellation formed by only one type of regular polygon.
Tessellations with Specific Attributes
If a tessellation contains the same arrangement of shapes and angles at each vertex it is uniform.
A uniform tessellation formed using two or more regular polygons is a semi-regular tessellation.
To determine if a semi-regular tessellation can be created from multiples of regular polygons test
that their interior angles sum to 360 degrees.
Determine whether a semi-regular tessellation can be created from regular nonagons and squares,
all having sides 1 unit long.
No, there are no whole number values for n and s, that 140n + 90s = 360.