Details

A prismatoid is defined to be the convex hull of two convex polygons in parallel planes. Therefore, a prismoid is a prismatoid where its two defining convex polygons are equiangular and oriented so that corresponding edges are parallel.

Whether a prismatoid can always be unfolded without overlapping edges is still an open problem, as is the case for general convex polytopes.

An example of a volcano unfolding of a prismoid that overlaps is given in [1, p. 323].

An example of an overlapping volcano unfolding of a nearly flat prismatoid with eight triangular faces is shown in [1, p. 324].

An example of an overlapping volcano unfolding of a nearly flat prismatoid with five faces is shown in [2].

References

[1] E. D. Demaine and J. O'Rourke, Geometric Folding Algorithms: Linkages, Origami, Polyhedra, New York: Cambridge University Press, 2007, pp. 321–324.

[2] I. Hafner. "Four Polyhedra, Each with an Unfolding that Overlaps Itself" from the Wolfram Demonstrations Project—A Wolfram Web Resource. demonstrations.wolfram.com/FourPolyhedraEachWithAnUnfoldingThatOverlapsItself.