'Prismatoid' ! Wow, that's a word that I _never_ learned in school. Thanks! In case anyone cares, the most general fundamental step in the 2D 'Quickhull' algorithm uses a _trapezoid/trapezium_ (Note to Wikipedia: NOT a triangle). Analogously, the most general fundamental step in the 3D 'Quickhull' algorithm uses a 'prismatoid' (NOT a tetrahedron). If you organize your Quickhull algorithm correctly, you don't have to worry about degenerate cases at all; e.g., you don't have to worry about repeated vertices, collinear vertices, etc. The correct 2D 'Quickhull' produces the hull points in cyclic order. This is important to the functioning of 3D 'Quickhull', where the 2 parallel convex polygons of a prismatoid must be 'merged' in the same cyclic order. --- Very cool insight by KQ Brown in 1979: you can compute 2D Voronoi diagrams with 3D convex hulls. Hint: stereographic projection! Brown, K.Q. "Voronoi diagrams from convex hulls". Info. Proc. Letters 9,5 (Dec. 1979), 223-228. This paper screams for a follow-on using quaternions for 3D/4D, but I haven't been able to find it. At 08:06 PM 8/3/2013, Bill Gosper wrote:

Prismatoid! I learned it from my grandmother's old math text. Its volume formula h*(Area(bottom)+4Area(midsection)+Area(top))/6 works for just about all the familiar solids (cones, spheres,...) --rwg. hgb>

What is the generalization of a (2D) trapezoid/trapezium to 3D?

I'm thinking of a convex polyhedron with 2 parallel faces, whose only other edges run between these 2 parallel faces.

I.e., we have the convex hull of 2 parallel planar polygons, not necessarily congruent or similar, and not necessarily with the same number of sides.

Is there a _name_ for such an object? (Hint: it _isn't_ a frustum, but some of the frustum formulae still work.)