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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.