Robinson Triangles
Robinson triangles, also known as golden triangles due to their close relation with the golden ratio discussed previously, make up the spikes of regular pentagrams.
A golden triangle is an isosceles triangle where a ratio between one of the identical sides $ a $ and the base $ b $ is the golden ratio $ \phi $.
A similar triangle to the Robinson triangle is the golden gnomon:
The golden gnomon is another isosceles triangle where a ratio between one of the identical sides $ a $ and the base $ b $ is the reciprocal of the golden ratio $ \frac{1}{\phi} $.
Regarding Penrose tiling, a golden triangle and two golden gnomons make up a regular pentagon, which ties in with the golden ratio local pentagon symmetry discussed earlier. P2 Penrose tiling are made from kites and darts. A kite is made from two golden triangles, and a dart is made from two gnomons.
Further Readings:
One final note – if you like proofs, you will enjoy this site: http://mrbertman.com/penroseTilings.html. It contains many definitions and theorems that deal with how to place a tile correctly (the site uses the term “legally”) and why those rules exist. You can even create your own Penrose tiling!
