Solid · Prisms and pyramids
Prismoid
Two parallel rectangular ends of different sizes joined by flat faces, as in a cutting, embankment or hopper.
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Dimensions
Results
volume V
Formulas
The prismoidal formula is exact whenever the cross-section area changes as a quadratic in height, which is true for any prismoid. M is the mid-height section, not the average of the ends.
Checked: the V formula agrees with a Monte Carlo measurement of the shape itself, made from its geometric definition, every time the site is built.
Topology lens
Topologically a ball. Its surface has V = 8 vertices, E = 12 edges and F = 6 faces, and V − E + F = 2, as for every convex polyhedron (Euler, 1758). More on the lens.