Decorative Penrose tile braid
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A 3D braid based on a decagon-shaped patch of a Penrose tiles.
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Updated at source:
Model information
- Source
- Printables
- Category
- Other Art & Designs
- License
- Creative Commons — Attribution — Noncommercial — Share Alike
This is intended to be decorative, rather than illustrating any mathematical properties. It is based on a way of decorating Penrose kite and dart tiles to construct braids. You can find a model for printing separate tiles here: https://www.printables.com/model/991628-penrose-kite-and-dart-covered-jigsaw-with-braids
To make this braid, I started with the following decagon found repeatedly in Penrose kite and dart tilings.
When the tiles are decorated with crossing paths, it looks like this:
The loose ends around the edges can be paired up and joined with additional tiles, forming eight closed paths, colored so they stand out.
The 3D print is layered so that distinct braids are separate when they cross. The whole model is a little flexible for this reason, though there is limited movement. I can't think of any practical application but it was fun to work on. When a Penrose tiling extends to fill the plain, these paths can become arbitrarily long, though many shorter ones like the circles occur frequently.