Difference between revisions of "Prism"
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| − | A [[Polyhedron|polyhedron]] for which two sides are | + | {{TEX|done}} |
| + | A [[Polyhedron|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|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). | ||
<img style="border:1px solid;" src="https://www.encyclopediaofmath.org/legacyimages/common_img/p074830a.gif" /> | <img style="border:1px solid;" src="https://www.encyclopediaofmath.org/legacyimages/common_img/p074830a.gif" /> | ||
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====Comments==== | ====Comments==== | ||
| − | In | + | 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==== | ====References==== | ||
<table><TR><TD valign="top">[a1]</TD> <TD valign="top"> B. Grünbaum, "Convex polytopes" , Wiley (1967)</TD></TR></table> | <table><TR><TD valign="top">[a1]</TD> <TD valign="top"> B. Grünbaum, "Convex polytopes" , Wiley (1967)</TD></TR></table> | ||
Latest revision as of 16:31, 11 April 2014
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) |
Prism. Encyclopedia of Mathematics. URL: http://encyclopediaofmath.org/index.php?title=Prism&oldid=31510