Investigation 12: Tessellation

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Presentation transcript:

Investigation 12: Tessellation Tessellations Investigation 12: Tessellation

Investigation 12: Tessellation Tessellations A tessellation is a design or pattern in which a shape is use repeatedly to cover a plane with no gaps, overlaps, or empty spaces. 1. A regular tessellation is a pattern made with only one type of regular polygon. 2. The sum of the measures surrounding a point (or vertex) must be 360°. 3. Only regular polygons that have an interior angle which is a factor of 360 will tessellate. Investigation 12: Tessellation

Can these figures form a regular tessellation? No. Although this is a regular polygon, it has an interior angle = 135°, which is not a factor of 360 Yes. This is a regular polygon with a 90° interior angle which is a factor of 360. Yes. This is a regular polygon with a 120° interior angle, which is a factor of 360. Investigation 12: Tessellation

Can these figures form a regular tessellation? Yes. This is a regular polygon with a 60° interior angle which is a factor of 360. No. This is not a regular polygon. It can tessellate but not in a regular tessellation. No. This is not a regular polygon. It can tessellate but not in a regular tessellation. Investigation 12: Tessellation

Semi-regular Tessellations If the same combination of regular polygons meet at each vertex, it is called a semi-regular tessellation. Investigation 12: Tessellation

Irregular Tessellations Other figures can make tessellations which are irregular. The figures used are irregular polygons and may be the same or different types. Here is an irregular tessellation made with kites and one with trapezoids. Investigation 12: Tessellation

Investigation 12: Tessellation Lizard (Tessellation 104) Investigation 12: Tessellation

Investigation 12: Tessellation Pegasus (Tessellation 105) Investigation 12: Tessellation

Tessellations by M.C. Escher Investigation 12: Tessellation

Investigation 12: Tessellation M. C. Escher, Cycle Investigation 12: Tessellation

Investigation 12: Tessellation Bulldog (Tessellation 97) Investigation 12: Tessellation

Special Notes on Tessellations 1. At each vertex of a tessellation, the sum of the measures of the angles must equal 360. 2. Any quadrilateral will tessellate. 3. Combinations of figures can be used to tessellate. 4. Only equilateral triangles, squares, and regular hexagons can make regular tessellations. Investigation 12: Tessellation