Penrose Chickens

Penrose Chickens were created by the mathematician Roger Penrose. They tile aperiodically... i.e. they tessellate, but the pattern never repeats. See https://en.wikipedia.org/wiki/Penrose_tiling

This is my own implementation of Penrose Chickens... the various examples I found on the Internet don't work :(, so I designed my own version, based on Penrose P2 (kite & dart) tiling.

Print Settings

Printer Brand:

Printrbot

Printer:

Rafts:

No

Supports:

Infill:

10% is fine

Post-Printing

If your printer isn't very accurate, you may need to sand/scrape the edges to make things fit. This seems to be particularly true around the beaks.

How I Designed This

This is based on the kite & dart (P2) tiling system. This design is a Public project at OnShape.com... go there and search for "Penrose Chickens". Feel free to copy it and remix.

Note that there are (and must only be) two different line shapes (one long, one short), which are rotated and translated to make up the sides of the kite and dart shapes. By changing these line shapes, you can make other objects which will also have the P2 tessellation property.

Someone might like to remix this so that the short lines (bottom of the kite bird, top of the dart bird) interlock, so that the whole tesselation locks together, in the same way that the beaks lock into their corresponding cutouts.

I offset the zero-tolerance outline of each object by 0.25mm, to allow for errors in printing. If you have a particularly accurate printer, you may want to reduce that to make for a tighter fit. Changing the offset by large amounts may cause the decoration lines on the top surface to screw up.

The bottom and top surfaces of both objects are also chamfered or filleted, so that any excesses around the edges of the top or bottom layers (hopefully) don't affect the fit.

Category: Math Art