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Prism (geometry) : ウィキペディア英語版
Prism (geometry)


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|bgcolor=#e7dcc3|Schläfli symbol||×
In geometry, a prism is a polyhedron with an ''n''-sided polygonal base, another congruent parallel base (with the same rotational orientation), and ''n'' other faces (necessarily all parallelograms) joining corresponding sides of the two bases. All cross-sections parallel to the base faces are congruent to the bases. Prisms are named for their base, so a prism with a pentagonal base is called a pentagonal prism. The prisms are a subclass of the prismatoids.
==General, right and uniform prisms==
A right prism is a prism in which the joining edges and faces are perpendicular to the base faces.〔William F. Kern, James R Bland,''Solid Mensuration with proofs'', 1938, p.28〕 This applies if the joining faces are rectangular. If the joining edges and faces are not perpendicular to the base faces, it is called an oblique prism.
For example a parallelepiped is an ''oblique prism'' of which the base is a parallelogram, or equivalently a polyhedron with six faces which are all parallelograms.
A truncated prism is a prism with nonparallel top and bottom faces.〔William F. Kern, James R Bland,''Solid Mensuration with proofs'', 1938, p.81〕
Some texts may apply the term rectangular prism or square prism to both a right rectangular-sided prism and a right square-sided prism. A ''right p-gonal prism'' with rectangular sides has a Schläfli symbol × .
A right rectangular prism is also called a ''cuboid'', or informally a ''rectangular box''. A right square prism is simply a ''square box'', and may also be called a ''square cuboid''. A ''right rectangular prism'' has Schläfli symbol ××.
An ''n''-prism, having regular polygon ends and rectangular sides, approaches a cylindrical solid as ''n'' approaches infinity.
The term uniform prism or ''semiregular prism'' can be used for a ''right prism'' with square sides, since such prisms are in the set of uniform polyhedra. A ''uniform p-gonal prism'' has a Schläfli symbol t. Right prisms with regular bases and equal edge lengths form one of the two infinite series of semiregular polyhedra, the other series being the antiprisms.
The dual of a ''right prism'' is a bipyramid.

抄文引用元・出典: フリー百科事典『 ウィキペディア(Wikipedia)
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