Призма: анықтамасы, түрлері және қасиеттері

Solid with 2 parallel n gonal bases connected by n parallelograms

In geometry, a prism is a polyhedron comprising an polygon base, a second base which is a translated copy (rigidly moved without rotation) of the first, and n other faces, necessarily all parallelograms, joining corresponding sides of the two bases. All cross sections parallel to the bases are translations of the bases. Prisms are named after their bases, e. g. a prism with a pentagonal base is called a pentagonal prism. Prisms are a subclass of prismatoids. Like many basic geometric terms, the word prism was first used in Euclid's Elements. Euclid defined the term in Book XI as “a solid figure contained by two opposite, equal and parallel planes, while the rest are parallelograms”. However, this definition has been criticized for not being specific enough in regard to the nature of the bases (a cause of some confusion amongst generations of later geometry writers).

An oblique prism is a prism in which the joining edges and faces are not perpendicular to the base faces. Example: a parallelepiped is an oblique prism whose base is a parallelogram, or equivalently a polyhedron with six parallelogram faces. A right prism is a prism in which the joining edges and faces are perpendicular to the base faces. This applies if and only if all the joining faces are rectangular. The dual of a right n prism is a right n bipyramid. A right prism (with rectangular sides) with regular n gon bases has Schläfli symbol { }×{n}. It approaches a cylinder as n approaches infinity.

A right rectangular prism (with a rectangular base) is also called a cuboid, or informally a rectangular box. A right rectangular prism has Schläfli symbol { }×{ }×{ }. A right square prism (with a square base) is also called a square cuboid, or informally a square box. Note: some texts may apply the term rectangular prism or square prism to both a right rectangular based prism and a right square based prism.

A regular prism is a prism with regular bases.

A uniform prism or semiregular prism is a right prism with regular bases and all edges of the same length. Thus all the side faces of a uniform prism are squares. Thus all the faces of a uniform prism are regular polygons. Also, such prisms are isogonal; thus they are uniform polyhedra. They form one of the two infinite series of semiregular polyhedra, the other series being formed by the antiprisms. A uniform n gonal prism has Schläfli symbol t{2,n}.

The symmetry group of a right n sided prism with regular base is [[Dihedral group of order 4n, except in the case of a cube, which has the larger symmetry group [[Octahedral symmetry of order 48, which has three versions of D4h as subgroups. The rotation group is Dn of order 2n, except in the case of a cube, which has the larger symmetry group O of order 24, which has three versions of D4 as subgroups. The symmetry group Dnh contains inversion iff n is even. The hosohedra and dihedra also possess dihedral symmetry, and an n gonal prism can be constructed via the geometrical truncation of an n gonal hosohedron, as well as through the cantellation or expansion of an n gonal dihedron.

A truncated prism is formed when prism is sliced by a plane that is not parallel to its bases. A truncated prism's bases are not congruent, and its sides are not parallelograms.

A frustum is a similar construction to a prism, with trapezoid lateral faces and differently sized top and bottom polygons.