Dodecagon tiling with rhombi - Tokyo 2020 emblem

Warm up

What is this ?

By dragging the green points on the grid in the dodecagon and rotating them with the circular vertex, try to tessellate the dodecagon with these three kind of pieces.

Be creative !

With this applet you can show the Varignon rectangle inside each rhombus by setting the opacity (blue) at max level and lowering that of the rhombi. When you're done, hide the grid and the points to make it look good. I'll share your artwork to the group afterwards. The Tokyo Olympics 2020 emblems are based on this construction

Squares

How many purple squares did you use ?

Check all that apply

Skinny rhombi (top left)

How many skinny rhombi did you use ?

Check all that apply

Medium rhombi (bottom left)

How many medium rhombi did you use ?

Check all that apply

Tokyo Olympics emblems

The Tokyo Olympics 2020 emblems are based on the following similar construction with a dodecagon twice as big, and a hole in it, the size of this dodecagon. Tokyo 2020 emblems : https://olympics.com/tokyo-2020/en/games/emblem/ See this geogebra applet to understand the emblem for the paralympics : https://www.geogebra.org/m/fhqxvgpj  See this article for more math about these emblems (spoiler) https://archive.bridgesmathart.org/2017/bridges2017-423.pdf