Prismatoid
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A prismatoid is a polyhedron where all vertices lie in two parallel planes. (If both planes have the same number of vertices, it is called a prismoid.)
If the areas of the two parallel faces are A1 and A3, the cross-sectional area of the intersection of the prismatoid with a plane midway between the two parallel faces is A2, and the height (the distance between the two parallel faces) is h, then the volume of the prismatoid is given by V = h(A1 + 4A2 + A3)/6.
[edit] Prismatoid families
Families of prismatoids include:
- Pyramids, where one plane contains only a single point;
- Wedges, where one plane contains only two points;
- Prisms, where the polygons in each plane are congruent and joined by rectangles or parallelograms;
- Antiprisms, where the polygons in each plane are congruent and joined by an alternating strip of triangles;
- crossed antiprisms;
- Cupolas, where 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;
- Quadrilateral-faced hexahedral prismatoids:
- Parallelepipeds - six parallelogram faces
- Rhombohedrons - six rhombi faces
- Hexahedral trapezohedra - six congruent rhombi faces
- Cuboids - six rectangular faces
- Quadrilateral frusta - an apex-truncated square pyramid
- Cubes - six square faces
