## A Radial Tessellation of Regular Pentagons and Rhombi

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Steps of this construction:

- Use the green circles and blue lines to construct the yellow pentagon, along with its green inscribed pentagram.
- Construct the equilateral triangle shown in gray. This is needed to obtain a twelve degree angle. The triangle is needed for its sixty degree angle, because 72 – 60 = 12. (The 72 degree angle is found inside the pentagon.)
- Identify the twelve degree angle shown in bold. A twelve degree angle is needed because 360 / 30 = 12.
- Use the red circles to complete the thirty sides of the regular triacontagon, which is shown with bold black segments, inscribed inside a large, bold, red circle.

This collection of curves was built around a tessellation of the plane using regular hexagons. To make the second version, I inverted the colors, except for the black circles and arcs.

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