parallellevyinen

Parallellevyinen is a geometric term used to describe objects whose cross-section remains unchanged when extended along a fixed direction. In two dimensions, a parallellevyinen region can be obtained by translating a fixed base shape along a straight line parallel to a chosen direction, producing a strip-like area with a constant cross-section. In three dimensions, a parallellevyinen solid is formed by extruding a planar base B along a straight vector v. The result is a prism, and every cross-section obtained by slicing with a plane perpendicular to v is congruent to B.

Key properties include that, if B has area A and the extrusion length is h, the volume is A·h. The cross-sections perpendicular to v are all congruent to B. For polygonal bases, the surface area equals the perimeter of B multiplied by h, plus twice the area A; for smooth bases, analogous formulas apply. This makes parallellevyinen objects predictable and easy to manufacture or model in computer graphics.

Examples commonly cited are a rectangular block (B a rectangle, extrusion perpendicular to its base) and a triangular prism (B a triangle). If the base is a circle, the extruded shape is the familiar cylinder in the idealized sense. While the term is not universally standard, it is used in some texts to describe prism-like forms with a constant cross-section along a fixed direction.

Parallellevyinen is closely related to the mathematical notions of prism and extrusion, and it is applicable in design, architecture, and manufacturing contexts where a uniform profile along length is desired. See also: prism, extrusion, cross-section.