In the upper half of Plate 63 Freese gave a 12-piece dissection of four pentagons to a decagonal ring. That dissection is actually hingeable, as I showed in Fig. I63b, EXCEPT that I neglected to show the hinge that would connect pieces 4 and 5. The missing hinge should be located at the point where those two pieces touch!
In the lower half of Plate 63 Freese gave a 20-piece dissection of ten pentagons to a decagonal ring. That dissection is not hingeable, and I wondered how many pieces would be needed if one asked for a hingeable dissection. Below is my 30-piece hinged dissection. Each pentagon is dissected into a trio of the same three pieces, and each trio is similarly hinged.
Copyright 2020, Greg N. Frederickson.
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Ernest Irving Freese's Geometric Transformations:
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Last updated June 30, 2020.