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In geometry, a **prismatoid** is a polyhedron whose vertices all lie in two parallel planes. Its lateral faces can be trapezoids or triangles.^{[1]} If both planes have the same number of vertices, and the lateral faces are either parallelograms or trapezoids, it is called a **prismoid**.^{[2]}

If the areas of the two parallel faces are *A*_{1} and *A*_{3}, the cross-sectional area of the intersection of the prismatoid with a plane midway between the two parallel faces is *A*_{2}, and the height (the distance between the two parallel faces) is h, then the volume of the prismatoid is given by^{[3]}

Pyramids | Wedges | Parallelepipeds | Prisms | Antiprisms | Cupolae | Frusta | ||
---|---|---|---|---|---|---|---|---|

Families of prismatoids include:

- Pyramids, in which one plane contains only a single point;
- Wedges, in which one plane contains only two points;
- Prisms, whose polygons in each plane are congruent and joined by rectangles or parallelograms;
- Antiprisms, whose polygons in each plane are congruent and joined by an alternating strip of triangles;
- Star antiprisms;
- Cupolae, in which the polygon in one plane contains twice as many points as the other and is joined to it by alternating triangles and rectangles;
- Frusta obtained by truncation of a pyramid or a cone;
- Quadrilateral-faced hexahedral prismatoids:
- Parallelepipeds – six parallelogram faces
- Rhombohedrons – six rhombus faces
- Trigonal trapezohedra – six congruent rhombus faces
- Cuboids – six rectangular faces
- Quadrilateral frusta – an apex-truncated square pyramid
- Cube – six square faces

In general, a polytope is prismatoidal if its vertices exist in two hyperplanes. For example, in four dimensions, two polyhedra can be placed in two parallel 3-spaces, and connected with polyhedral sides.

**^**Kern, William F.; Bland, James R. (1938).*Solid Mensuration with proofs*. p. 75.**^**Alsina, Claudi; Nelsen, Roger B. (2015).*A Mathematical Space Odyssey: Solid Geometry in the 21st Century*. The Mathematical Association of America. p. 85. ISBN 9780883853580.**^**Meserve, B. E.; Pingry, R. E. (1952). "Some Notes on the Prismoidal Formula".*The Mathematics Teacher*.**45**(4): 257–263. JSTOR 27954012.

- Weisstein, Eric W. "Prismatoid".
*MathWorld*.