Not long after this book appeared, Gavin improved on my improvement of Freese's concave {16} to a square. Where I had been content to reuse Freese's completing the tessellation method, Gavin came up with a different way to complete the tessellation, and thereby saved yet another piece. Also, I think that Gavin's dissection is more attractive than the one I included in the book.
Gavin sliced the four points off of the concave {16} and then nestled them in the cavities of what remained. The resulting element needs only a small square in order to become a tessellation element. And of course this small square and a square equivalent to the concave {16} also make a tessellation element. Gavin realized that you can overlay the two elements as above so that only one piece other than that one large piece will get cut. The resulting 10-piece dissection appears below.
In September 2005, Gavin Theobald sent me an 8-piece dissection of two hexagons to one, with three pieces turned over. This beats Freese's 9-piece dissection in Manuscript 3, if you allow turning over (which Freese didn't). I should have included a reference to Gavin's dissection in this section, but I had already written the section and just forgot. (Sorry, Gavin!)
Copyright 2007, Greg N. Frederickson.
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Piano-hinged Dissections: Time to Fold!
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Last updated March 5, 2007.