Shortly before this book appeared, I improved one of the results on Table 4.1. I found a 12-piece twist-hinged dissection of a hexagram to a square, improving on the 13-piece solution listed. Converting all twist hinges to piano hinges, this leads to an improvement in the corresponding piano-hinged dissection, from 28 to 26 pieces.
The 12-piece dissection results from a 10-piece swing- and twist-hinged dissection that has two swing hinges. Taking advantage of some mirror-image symmetry, I can convert the two swing hinges and their adjacent pieces into four piano-hinged pieces. Applying the twist-to-piano conversion will then yield a 24-piece piano-hinged dissection.
In March 2007, I improved one of the results on Table 4.1. I found a 7-piece twist-hinged dissection of a Latin Cross to a square, improving on the 11-piece solution listed. Converting all twist hinges to piano hinges, this leads to an improvement in the corresponding piano-hinged dissection, from 22 to 16 pieces.
There are two nonconvex pieces that have two twist hinges, and these seem to each require two additional pieces rather than the one additional piece required by the other five pieces.
Copyright 2006-2007, Greg N. Frederickson.
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Piano-hinged Dissections: Time to Fold!
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Last updated March 21, 2007.