In Ernest Freese's manuscript, Geometric Transformations (completed before his death in 1957), which I got access to in February 2003, there is (on Plate 158) a generalization of the Greek Cross as in Figure 12.15 and a 5-piece dissection of the generalized cross into a square, as suggested by Figure 12.16. Freese even noted the hinge points between the four pieces that are congruent. Too bad that I didn't get this help a bit sooner, while I was still writing the book!
Copyright 2003, Greg N. Frederickson.
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Hinged Dissections: Swinging & Twisting
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Last updated February 27, 2003.