The Manifold Beauty of Piano-hinged Dissections

Greg N. Frederickson
Renaissance Banff: Mathematics, Music, Art, Culture (2005)
Pages 1–8


A geometric dissection is a cutting of one geometric figure into pieces that we can rearrange to form another. For some dissections, it is possible to hinge the pieces together, so that we can flip the pieces one way on the hinges to form one figure, and flip them another way to form the other figure. When the hinge connects two pieces along a shared edge in both target figures, the movement corresponds to a folding. We call such dissections piano-hinged dissections. This paper explores design methods and properties of piano-hinged dissections.