Now that we have had a quick introduction to piano-hinged dissections, it’s time to slow down and think more carefully about them. Before we invest too much energy in finding them, we should make sure that they have a sound mathematical foundation. Also, it would be nice to develop some appreciation for the special properties that piano-hinged dissections can exhibit. Otherwise, why make such a big flap? Let’s start by refining our model of piano-hinged dissections, and then explore the properties of a specific example. That will lead us to survey a variety of cyclic hingings and conclude the chapter by considering some additional properties.