Tessellation of an Equilateral Pentagon

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Tessellating Equilateral Pentagon This simple tessellating pattern features an equilateral pentagon, four of which form a hexagon. While it's not a regular pentagon, its properties make it quite interesting. Within each pentagon, you'll find two right angles, with the other three angles waiting to be calculated. To start, I figured out the measure of one of the two congruent angles, and that's 45° plus arccos(sqrt(2)/4). By mirroring my sketches, I created a nice starting design project for students. Included are two shelled pentagons, a pentagonal caddy, and a hexagonal caddy. The edge length of each pentagon is 25 mm, with a thickness of 3.6 mm. The caddies stand at 60 mm tall.