PRISMATOID

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.

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Prismatoid families

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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

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