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A hexadecagon is a sixteen-sided polygon. Hexadecagons are very popular in art and architecture.

13. Century Iranian Eight-Pointed Star-Shaped Tiles from the MET Museum Archive
Saddlebag weaved by the Shahsevan nomads, from Northwestern Iran or Azerbaijan from the Met Museum Archive

Concave hexadecagons (also called 8-pointed stars) are very famous in different religions and cultures. Concave Hhexadecagons can be in many different shapes. Here are three examples.

Let's explore these hexadecagons.

  • Measure the side length of each.
  • Can you find the areas of each shape by using the blue unit square?
  • If the area of the green shape is A, express the others in terms of A. (Hint: you may try to drag the hexadecagons on top of each other to compare their areas.)

Using this canvas, create your own design for tiles and use them to create tilings;