Namespaces
Variants
Actions

Prism

From Encyclopedia of Mathematics
Jump to: navigation, search

A polyhedron for which two sides are $n$-gons (the bases of the prism), while the other $n$ sides (the lateral sides) are parallelograms. The bases are congruent and located in parallel planes. A prism is called direct if the planes of the lateral sides are orthogonal with the planes of the bases. A direct prism is called regular if its bases are regular polyhedra. A prism is called triangular, rectangular, etc., depending on whether the bases are triangular, rectangular, etc. Six-angled prisms are shown in the figures (Fig. a shows a direct prism). The volume of a prism is equal to the product of the area of one of its bases and its height (the distance between the bases).

Figure: p074830a

Figure: p074830b


Comments

In $d$-space a prism is the vector-sum of a $(d-1)$-polytope and a segment which is not parallel to the affine hull of the $(d-1)$-polytope.

References

[a1] B. Grünbaum, "Convex polytopes" , Wiley (1967)
How to Cite This Entry:
Prism. Encyclopedia of Mathematics. URL: http://www.encyclopediaofmath.org/index.php?title=Prism&oldid=31510
This article was adapted from an original article by BSE-3 (originator), which appeared in Encyclopedia of Mathematics - ISBN 1402006098. See original article