Engraved Penrose P3 Tiles, Mathematical buying Puzzle, Pentagon, Tile Puzzle, Physics Puzzle, 89 golden diamonds, 55 lozenges, Pattern Blocks, STEM

» Have fun creating amazing tile patterns
» Laser cut for mathematical precision
» All side are one inch long
» 144 tiles: 89 golden diamonds & 55 golden lozenges

With a box of squares how many ways can you tile a flat surface without leaving gaps? While you can slide each row (or column) back and forth, there isn't much else. Something similar happens if you use equilateral triangles. Would you believe that Sir Roger Penrose's P3 set tiles can create an infinite number of tile patterns?

Following in the footsteps of previous explorers, Penrose discovered a group of patterns descended from the pentagon and the golden ratio. His third set is composed of only two tiles, the golden diamond and the golden lozenge. He called them thin and thick rhombs. In the patterns formed, the tiles are used in the golden ratio to each other. This means that for every golden lozenge used, there are 1.61803398… golden diamonds in the pattern. The golden ratio, phi, is a non-repeating non-terminating decimal, like pi. This non rational relationship implies that the pattern never repeats! So like a fractal, how you start the pattern gives buying you a different result.

With these beautiful tiles you will have fun exploring many possibilities. The backs are stained to add additional variety and options for pattern creation. By matching the patterns on the light side of the tiles you will construct a P3 tiling!

As my own contribution, I have invented a system of paths for the P2 and P3 sets. These markings maintain the original constraints of the arc and circle pattern, but create a measure of connection between P2 and P3 allowing for some additional fun pattern making by mixing the two together.

Inquiries and special orders are welcome.

Learn more about Penrose tiles through these cool videos!
https://www.youtube.com/watch?v=48sCx-wBs34
https://www.youtube.com/watch?v=QTrM-UVcgBY
https://www.youtube.com/watch?v=th3YMEamzmw
https://www.youtube.com/watch?v=yxlEojkVJ0c
https://www.youtube.com/watch?v=jJnEIjqbkR4

They are laser cut from 1/8" toy grade Baltic Birch plywood

Not for children under the age of 3.