Ingeometry, a prismatoid is a polyhedron whose vertices all lie in two parallel planes. Its lateral faces can be trapezoidsortriangles.[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 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[3]
Pyramids | Wedges | Parallelepipeds | Prisms | Antiprisms | Cupolae | Frusta | ||
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Families of prismatoids include:
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.
Convex polyhedra
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Platonic solids (regular) |
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Catalan solids |
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Dihedral regular |
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Dihedral uniform |
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Dihedral others |
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Degenerate polyhedra are in italics. |
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