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Mathematics LibreTexts

2. Regular Tilling

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    Goal: To appreciate polygons and support the idea that there are three regular polygons that be tessellated.


    • A polygon is a closed 2-dimensional figure with straight sides

      • An n-gon is a polygon with exactly n sides

      • A regular n-gon is a polygon with exactly n sides, where all sides are of equal length and all interior angles of the polygon are equal. The sum of the interior angles of a regular n-gon is 180°(n - 2). It follows that each interior angle must measure 180°(n - 2)/n. So:

        • A regular 3-gon is an equilateral triangle. Each interior angle is 60°

        • A regular 4-gon is a square. Each interior angle is 90°

        • A regular 5-gon is a regular pentagon. Each interior angle is 108°

        • A regular 6-gon is a regular hexagon. Each interior angle is 120°

        • A regular 7-gon is a regular heptagon. Each interior angle is 900/7°, or approximately 128.6°

        • A regular 8-gon is a regular octagon. Each interior angle is 135°


    Suppose I want to tape the same regular n-gons together to make 2-dimensional shapes. What are my options? I don’t want to bend or fold the n-gons. Let’s just concentrate on the corners of these objects.