Reckoning / Shape / Truncated pyramid (frustum)
Solid · Prisms and pyramids
Truncated pyramid (frustum)
A square pyramid with its top cut off parallel to the base.
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Dimensions
Results
volume V
Formulas
The big pyramid minus the small one cut off; the algebra collapses to the formula above, known to Egyptian scribes about 1850 BC.
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.