Prismatoid

Prismatoid

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.

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:
*# 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

External links

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Look at other dictionaries:

  • prismatoid — PRISMATOÍD, prismatoide, s.n. Corp cu o formă apropiată de aceea a unei prisme (1) [pr.: to id] – Din fr. prismatoïde. Trimis de ana zecheru, 09.04.2004. Sursa: DEX 98  prismatoíd adj. m. (sil. to id), pl. prismatoízi; f …   Dicționar Român

  • Prismatoid — (Prismoid), ein Polyeder, begrenzt von zwei Polygonen (Grundflächen) in parallelen Ebenen, deren Seitenzahlen m und n verschieden sein können, und von m + n Dreiecken (Seitenflächen), von denen jedes eine Ecke mit der einen, die Gegenseite mit… …   Lexikon der gesamten Technik

  • Prismatoid — (griech., »einem Prisma ähnlich«, Trapezoidalkörper), ein zur Klasse der Polyeder gehöriger Körper, den man erhält, wenn man in zwei parallelen Ebenen zwei geradlinige Polygone von gleich vielen Seiten (die Grund und die Deckfläche) derart… …   Meyers Großes Konversations-Lexikon

  • Prismatoid — Prismatoīd, s. Prismoid …   Kleines Konversations-Lexikon

  • prismatoid — [priz′mə toid΄] n. a polyhedron with all of its vertices in two parallel planes, as a pyramid or prism …   English World dictionary

  • Prismatoid — Ein Prismatoid oder Prismoid ist ein geometrischer Körper. Es handelt sich um ein Polyeder mit parallelen Vielecken als Grund und Deckfläche sowie Dreiecken oder Trapezen als Seitenflächen. Im Unterschied zum Prisma brauchen Grund und Deckfläche… …   Deutsch Wikipedia

  • prismatoid — noun a polyhedron whose vertices all lie in one or the other of two parallel planes; the faces that lie in those planes are the bases of the prismatoid • Hypernyms: ↑polyhedron • Hyponyms: ↑prismoid …   Useful english dictionary

  • prismatoid — noun Etymology: Late Latin prismat , prisma prism Date: circa 1890 a polyhedron that has all of its vertices in two parallel planes …   New Collegiate Dictionary

  • prismatoid — /priz meuh toyd /, n. Geom. a polyhedron having its vertices lying on two parallel planes. [1855 60; < Gk prismat (s. of prîsma) PRISM + OID] * * * …   Universalium

  • prismatoid — noun Any polyhedron whose vertices all lie in either of two parallel planes …   Wiktionary

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