The Dutch graphic artist M.C. Escher was absolutely obsessed by mathematical patterns, and they play an important part in many of his famous artworks;
Jill Briton might just be equally obsessed with mathematical patterns, and she even wrote a book about it: "Investigating Patterns, Polyhedra Pastimes" (ISBN 978-0769027821)
On her website, she uploaded a teaser for the book, namely a papercraft kaleidocycle (a polyhedra ring toy that you can infinitely turn in on itself!) based on M.C. Escher's Lizard/Fish/Bat tessellation:
Download + build your own papercraft M.C. Escher kaleidocycle (by Jill Briton):
https://web.archive.org/web/20170623111515/http://britton.disted.camosun.bc.ca/jbescher6.htm
(click the "B/W" or "Color" links near the bottom of the page)
If you need some extra help on how to assemble the kaleidocycle, have a look at this instructional video by Sylvia Nitsche (you can download that pattern too from her website: link )
Have fun! ;o)
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