# Penrose tiles and the great icosicosidodecahedron

Last night we completed a fun day of playing around with our Zometool set by building a great icosicosidodecahedron :

A large part of the fun from just playing around with the Zome pieces is that you never know what shapes you’ll end up with! After we finished building this monstrosity something very surprising happened. My younger son was looking at the structure and said that he saw shapes in it that looked like the shapes of Penrose tiles. We have talked about Penrose tiles before, but it was back in March:

Penrose Tiles and some simple 3d Variations

I honestly have no idea why these shapes stuck with him, but kids surprise you sometimes.

Tonight we looked up the angles in the Penrose darts and kites and then did a short calculation of the angles in the great icosicosidodecahedron. The main tool you need is that the angles in a triangle add up to 180 degrees, so that was easy enough to explain to him. To my great delight he was correct – the shapes he saw were indeed exactly the shapes of the Penrose tiles.

Another example of why I love teaching my kids 🙂