Design Nomenclature / Form & Geometry
Genus
Also called euler characteristic, handle count, holes
This entry has not been translated yet and is shown in English.
The number of handles on a closed orientable surface — holes you could thread a string through, not dents or openings. A sphere is genus 0, a torus 1, a two-handled cup 2. Euler's formula fixes it exactly: V − E + F = 2 − 2g, regardless of how dense the mesh is or how its edges run.
In practice
The one sense in which topology is a hard property of a model rather than a matter of taste. A boolean that punches a through-hole changes the genus; one that dents the surface does not, however dramatic it looks.