Facetiness

Facetiness is a descriptive term used to characterize the extent to which an object or concept displays distinct planar surfaces, or facets, across different disciplines. It is not a formal scientific term with a single universal definition, but rather a flexible descriptor employed to convey the degree of surface flatness, facet-richness, or multi-faceted character in a given context.

In geometry and crystallography, facets refer to the flat faces of polyhedra or crystal forms. Facetiness here tends to correlate with the number and prominence of these faces: more faces generally imply higher facetiness, while a smooth, curved form manifests low facetiness. A cube has lower facetiness than a dodecahedron, and a geodesic sphere has high facetiness due to its many small faces.

In computer graphics, facetiness describes how polygonal a model appears. High facetiness produces a visibly faceted or blocky look, especially with flat shading, whereas smoothing or subdivision reduces facetiness, yielding a smoother surface. The term is often used in critique of low-resolution meshes or in discussions of level-of-detail rendering.

In data visualization and analysis, facetiness can be used metaphorically to describe how many distinct aspects or facets a dataset, topic, or model encompasses. There is no standardized metric, but potential indicators include the number of facets (faces) in a geometric proxy, surface-area-to-face ratios, or the distribution of surface normals when approximating curved forms.

Overall, facetiness serves as a practical shorthand for describing the complexity or plurality of planar features in a given object or concept.