Other meanings of PRISM
Geometry
In geometry, a prism is a polyhedron with two congruent, parallel faces (bases) and other faces (lateral faces) that are parallelograms. Prisms are classified by the shape of their bases—triangular, pentagonal, and so on—and are a fundamental class of polyhedra studied since antiquity.1
A prism is a polyhedron whose bases are congruent polygons in parallel planes, and whose lateral faces are parallelograms. If the lateral faces are rectangles (i.e., the bases are perpendicular to the lateral edges), the prism is a right prism; otherwise it is oblique. The volume of any prism is the product of the base area and the height (the perpendicular distance between bases), a formula known since Euclid.2
The surface area consists of the two base areas plus the lateral area. For a right prism, the lateral area equals the perimeter of the base times the height. Prisms satisfy Euler's formula V − E + F = 2; for an n-gonal prism, V = 2n, E = 3n, and F = n+2.3
Prisms are named by their base polygon: triangular, rectangular, pentagonal, hexagonal, etc. A rectangular prism with square bases is a cube; a rectangular prism with all faces rectangles is a cuboid. A prism whose bases are regular polygons and whose lateral edges are perpendicular to the bases is a uniform prism.4
An antiprism is a related polyhedron with alternating triangles instead of parallelograms, and a trapezohedron is its dual. Prisms are also examples of prismatoids, polyhedra whose vertices lie in two parallel planes.5
Prisms appear throughout science and engineering. In optics, a triangular prism disperses light into a spectrum, a phenomenon exploited by Newton.6 In architecture, prismatic forms are common in buildings and columns. In crystallography, crystal habits often form prismatic shapes, such as hexagonal prisms in quartz.7
In mathematics, prisms are used to illustrate volume integration and are fundamental in the study of polyhedra and tessellations. The prism graph is a graph-theoretic representation of a prism's vertices and edges.8
Beyond the familiar right prisms, oblique prisms have lateral faces that are non-rectangular parallelograms, and their volume is still base area times height. A parallelepiped is a prism whose bases are parallelograms, and a rhombohedron is a parallelepiped with rhombus faces.5
Prisms are also studied in higher dimensions: a 4-dimensional prism is a hyperprism (or duoprism), formed by the Cartesian product of two polygons. The concept extends to any dimension, and such polytopes are called prismatic polytopes.8 In the history of mathematics, the ancient Greeks, including Euclid, defined prisms and proved their volume formulas, but the term itself derives from the Greek prisma, meaning "something sawed," referring to the shape of a sawed log.1
The term 'prism' derives from the Greek 'prisma' (something sawed), reflecting the shape of a sawed log.
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