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A Family of Non-Periodic Tilings, Describable Using Elementary Tools

76 joshu 8 6/10/2025, 7:47:37 PM arxiv.org ↗

Comments (8)

jameshart · 1d ago

Someone needs to get this into the hands of a ceramic tile manufacturer or a manufacturer of pavers. These are some of the most immediately aesthetically useful tile shapes mathematics has produced since the hexagon.

ThalesX · 1d ago

Ever since those Einstein tiles I've been dreaming about making a company that does these kind of fancy tiling.

noqc · 1d ago

>aesthetically useful

jameshart · 1d ago

Yes?

Useful for making aesthetically pleasing things.

0y · 1d ago

"The pattern shown in Figure 5(b) was originally presented by Jan Sallmann-Räder in a social media post"

this seems to be said post: https://www.facebook.com/share/1DJu7tSjKq/

joshu · 1d ago

yeah, miki also posts in https://www.facebook.com/groups/tiling as well. i've been following this for a few weeks

tocs3 · 14h ago

So, how do these tiles differ from other non periodic tiling? I have looked at but not read the paper. It could be a little over my head.

joshu · 1d ago

Full title: A Family of Non-Periodic Tilings, Describable Using Elementary Tools and Exhibiting a New Kind of Structural Regularity

This is Miki Imura’s spiral tesselation.