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Prismatoid

From Wikipedia, the free encyclopedia

A prismatoid is a polyhedron where all vertices lie in two parallel planes. (If both planes have the same number of vertices, and the lateral faces are either parallelograms or trapezoids, 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, or, the second plane contains two more 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:
1. Parallelepipeds - six parallelogram faces
2. Rhombohedrons - six rhombi faces
3. Trigonal trapezohedra - six congruent rhombi faces
4. Cuboids - six rectangular faces
5. Quadrilateral frusta - an apex-truncated square pyramid
6. Cubes - six square faces

[edit] External links

Eric W. Weisstein, Prismatoid at MathWorld.

This polyhedron-related article is a stub. You can help Wikipedia by expanding it.

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