Ovoid

Ovoid is an adjective describing something egg-shaped: elongated and rounded with a tapering end, often resembling the form of a bird’s egg. The noun form refers to an object that has this egg-like shape. The word derives from the French oeuf, meaning egg. In everyday language, ovoid describes a wide range of natural and manufactured objects, such as eggs, certain fruits and seeds, or decorative items that have an egg-like profile.

In geometry, an o void refers to a three-dimensional shape that resembles an egg. Broadly, it denotes any compact, strictly convex body whose boundary is smoothly curved, though the term is sometimes used more loosely for shapes that are not perfect ellipsoids. An ellipsoid is a common, precise example of an ovoid, but not all ovoids are ellipsoids; they may deviate from perfect symmetry while maintaining an overall egg-like form.

In finite geometry, an ovoid is a specific kind of configuration in projective space. In three-dimensional projective space PG(3,q), an ovoid is a set of q^2+1 points with the property that no three are collinear (equivalently, every line meets the ovoid in at most two points). Elliptic quadrics in PG(3,q) provide standard examples of ovoids, and for certain values of q other ovoids exist as well.

The term is widely used across disciplines to describe egg-shaped forms, from biological specimens and seeds to architectural or mechanical designs and abstract geometrical shapes. The exact meaning varies with context, ranging from everyday descriptive usage to precise mathematical definitions.