Prism (geometry)

A prism ( plural: prisms) is a geometrical body, which has a polygon as a base and the side edges are parallel and equal in length.

A prism formed by parallel translation of a polygon along a planar not situated in this plane straight line in space, and is therefore a specific polyhedron. One can also speak of an extrusion of the polygon.

Straight and oblique prism

If the parallel shift of the polygon perpendicular to the base, it is called a right prism otherwise of an oblique prism.

Designations

The given polygon is called the base, the other to congruent and parallel boundary area than the top surface. The total of all remaining boundary areas is outer surface. This consists of parallelograms in the special case of a right prism of rectangles.

Classification

The prism is a special case of the cylinder. A special form of the prism is the cuboid. He's from each side considered a prism. In the strict sense is understood in optics under a prism usually a right prism with a triangle as the base, see Prism (optics).

Formulas for volume and surface coat -

The volume of a prism is given by

Wherein the surface area of ​​the footprint and the height of the prism respectively. The principle of Cavalieri says that two prisms (about a straight and a distorted prism) with the same base and height have the same volume.

The lateral surface of a right prism is given by

Wherein represents the perimeter of the base and the height of the prism. The entire surface of the prism is given by

Where and are the contents of primary and lateral surface correspond.

Bipyramid

If you connect all the centroids of those faces of a polyhedron with each other, which have common vertices, then one obtains the dual polyhedron to the body.

The dual body of a right prism with a polygonal base is a bipyramid with a similar mirrored pyramid. The surface area is calculated as follows:

Antiprism

Unlike a prism lie with the anti- prism top and bottom, which consist of a regular n-gon, parallel but twisted around each corner to edge. The jacket case form 2n isosceles triangles.

A simple example of an anti- prism is the octahedron, which can be regarded as anti- prism with a triangular base. The octahedron is also a bipyramid with a square base.