Penrose Aperiodic Rhombs

A nice version of Penrose Tilings is available here: 
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Penrose Aperiodic Rhombs: a famous aperiodic tiling with just two shapes- a pair of rhombuses with equal sides, but with the ratio of their areas made to equal the golden ratio. Note that although the starting pattern of 10 tiles is symmetrical, adding any further tiles breaks the symmetry, as highlighted by the path of the double curves. Sir Roger Penrose- who just won the Nobel prize in physics for his contributions to General Relativity- also discovered tessellations (tilings) that are aperiodic even though the two tile types are regularly shaped polygons. If one tries to shift a part of a Penrose tiling, the shifted part will not align or match up with any other part of the same tiling- all the way out to infinity! In this construction, single and double line patterns must align such that the tiles can only connect in specific ways to ensure the non-repetitive nature of the Penrose tiling structure. Shown here is one way these two tile types will fill the plane.

Wikipedia has the details on Penrose Tilings and their inventor Sir Roger Penrose (Recently won Nobel Prize!) 

Penrose Tiling Puzzle

This puzzle was produced and sold in the 1990s. 
Wikipedia has the details on Penrose Tilings and their inventor Sir Roger Penrose (Recently won Nobel Prize!) 
A nice basic version of Penrose Tilings is available here: 
From Etsy: BUY NOW Penrose Tiles 

Note: this site contains affiliate links for which I may be compensated

Penrose Tiling Puzzle: a challenging puzzle with pieces that come in only two shapes. Sir Roger Penrose- who just yesterday won the Nobel prize in physics for his contributions to General Relativity- also discovered tessellations (tilings) that are aperiodic even though the two tile types are regularly shaped polygons. If one tries to shift a part of a Penrose tiling, the shifted part will not align or match up with any other part of the same tiling- all the way out to infinity! This puzzle, entitled “Perplexing Poultry”, created and sold by Penrose himself, uses polygons modified into crazy looking birds such that the tiles can only connect in specific ways to ensure the non-repetitive nature of the Penrose tiling structure. Shown here is one way these two tile types will fill the plane.