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Hexadecagons

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.

https://mathigon.org/polypad/JhZVidPU2qAYLg

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.)
https://mathigon.org/polypad/9wXiLNTiDndsTw

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

https://mathigon.org/polypad/VGxD8UDYQzEVdA