Penrose P2 tessellation tiles

prusaprinters

(Penrose P2 tiling diagram by Tovrstra at English Wikipedia, CC BY-SA 3.0)Whether you're celebrating Phi (φ) Day or any other holiday, these Penrose P2 tiles will be a conversation starter!About Penrose tilingPenrose tiling is a non-periodic tessellation using two shapes to create intricate and interlocking designs. There are a few Penrose tile types, with the “P2” type being the most commonly discussed. The two tile shapes in P2 are often called “kites” and “darts.” The tiles are arranged in a pattern that is not periodic but can appear to be when viewed from a distance, leading it to be called a “quasiperiodic” pattern. Penrose tilings were first discovered/invented by Nobel Prize laureate physicist and mathematician Roger Penrose in the 1970s. The patterns have been significantly studied in the fields of mathematics and physics, leading to a better understanding of physical materials that form quasicrystals. Learn more about Penrose tiling at Wikipedia. About this renditionThis design includes embossed circular arcs that enforce the non-periodic pattern. Their radii follow the Golden Ratio. Make sure the arcs fit together when you arrange the tiles, so that they make a smooth curve as in the diagram above.Printing and assemblyPhotos coming soon.No supports are needed.When making tiles, bear in mind that for tiling purposes you'll need more kites than darts – an infinite plane filled with these tiles will require φ (~1.618) kites per dart.  The .3mf file includes both tiles. There are two main .3mf files for different sizes. Each file includes one kitew and one dart, so you can print however many of each by copying and pasting them in your slicer app. The “large” file has a kite tile with about 3" across the longest dimension. The “small” file has a kite tile with about 3 cm across the longest dimension. You can definitely print a lot more small tiles than large ones in a given timeframe, and assemble much more of the pattern in a given space. Personally I find the larger ones more fun and satisfying to play with though. You may wish to print the kites and darts in their own colors. I have included two gcode files with five kites and five darts each in the larger scale. The print time shown is to print both sets for a total of 10 large tiles. I printed these with PLA on my MK3/S+, using 0.4 mm nozzle, 0.2 mm layer height with “speed” setting of 20% grid infill. You might be able to go with thicker layers and/or less infill to speed things up. If you have any trouble that I can help with, please let me know, and I'll be happy to make modifications. Please post your makes!