  An example of reversible (or hinge inside-out transformable) figures is the
Dudeney's Haberdasher's puzzle in which an equilateral triangle is dissected
into four pieces, then hinged like a chain, and then is transformed into a
square by rotating the hinged pieces. Furthermore, the entire boundary of each
figure goes into the inside of the other figure and becomes the dissection
lines of the other figure. Many intriguing results on reversibilities of
figures have been found in prior research, but most of them are results on
polygons. This paper generalizes those results to a wider range of general
connected figures. It is shown that two nets obtained by cutting the surface of
an arbitrary convex polyhedron along non-intersecting dissection trees are
reversible. Moreover, a condition for two nets of an isotetrahedron to be both
reversible and tessellative is given.
