The Prismatoid and the Prismoidal Formula

The General Prismatoid

A general prismatoid is a solid such that the area of any section, say Ay, parallel to and distant y from a fixed plane can be expressed as a polynomial of y of degree not higher than the third.



A solid is a general prismatoid if

$A_y = a + b_y + cy^2 + dy^3$

Where a, b, c, and d are arbitrary constants which may be positive, negative, or zero.