frustumlike

Frustumlike describes objects that resemble a frustum—a solid formed by cutting a cone or pyramid with two parallel planes. In this informal sense, a frustumlike body has two parallel bases, often polygonal or circular, and a tapering lateral surface that connects corresponding points on the bases. If the bases are similar polygons and the side faces are planar, the solid is a frustum of a pyramid; if the bases are circles, it is a frustum of a cone. More generally, frustumlike shapes may be polyhedra or curved-surface solids whose vertices lie between two parallel planes and whose cross-sections parallel to the bases are similar to the bases.

The essential measurements are the height, the distance between the two bases, and the sizes of the bases. For a frustum of a cone with base radii r1 and r2, the volume is V = (1/3) π h (r1^2 + r2^2 + r1 r2). For a frustum of a pyramid with base areas A1 and A2 (which are similar), the volume is V = h (A1 + A2 + sqrt(A1 A2)) / 3. In both cases, cross-sections parallel to the bases are similar to the bases, and the lateral surface is formed by lines or curves that connect corresponding points on the two bases.

Frustumlike shapes appear in architecture, product design, and modeling, where a tapered or truncated form is desirable. They are also used in computer graphics to describe bounding volumes or objects that approximate a frustum for purposes such as perspective projection or view frustum culling. The term is informal and covers variants that closely, but not perfectly, fit the mathematical definition of a frustum.