Penrose tiling P2 tessellation cookie cutters

(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, cookies cut with these Penrose P2 tile cookie cutters will be a conversation starter!

About Penrose tiling

Penrose 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 rendition

This design includes debossed circular arcs that enforce the non-periodic pattern. Their radii follow the Golden Ratio. Make sure the arcs fit together when you arrange your cookies to make a smooth curve, as in the diagram above.

Printing and assembly

When making cookies, 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 cookie cutters. The cookies are about 3 inches across the longest dimension.

No supports are needed.

I recommend printing in PETG or polypropylene. PLA and ASA are not great for food. 

Making 3D prints truly food-safe is not trivial, as the prints are somewhat porous and can harbor bacteria. But you know, so can wood. But to minimize any risk, I recommend using the ironing print setting on the uppermost top layer to seal up any gaps (the print file .gcode attached to this model has ironing the top layer set). Clean carefully between uses and if you want to learn more about the topic of food safety in 3D printing, check out this article. 

Baking notes

Dough may get a little stuck in the narrow corners when the dough is soft (i.e., when it is close to room temperature). Be sure to cool your dough, and if you have trouble extricating these parts, a little flour dusting on the interior of the cutters can help. 

Change log

• 2023-01-18 New “punch” models are now available for download. These will punch out the dough from the cutter. The punch is shaped exactly like the inside of the cutter, so it will smoothly push your dough out while retaining its shape. 
• 2023-01-22 More tolerance added to punches.

Print photos and cookie photos are coming soon!