# Genus (mathematics) > [[PORTAL_Graph_theory|Graph theory]] spine. ## Microsims — three.js <div class="microsim-player"> <iframe src="https://wikitube-3d-microsims.netlify.app/Genus_mathematics_microsim.html" width="100%" height="520" frameborder="0" loading="lazy" sandbox="allow-scripts allow-same-origin" title="Genus (mathematics) — three.js microsim"></iframe> </div> <p class="wt-pending"><strong>Note:</strong> staged, awaiting CDN deploy.</p> In mathematics, the genus of a connected, orientable surface is the number of "handles" it has — informally, the number of holes that pass all the way through it. A sphere has genus 0, a torus has genus 1, a two-holed torus has genus 2, and so on; genus is the single number that, together with orientability, completely classifies closed surfaces up to continuous deformation. ## Overview This build renders surfaces of increasing genus side by side so the "number of handles" definition is visible directly rather than described abstractly. Genus also shows up outside pure topology: in [[Graph_theory|graph theory]], the genus of a graph is the minimum genus of a surface on which the graph can be drawn without any edges crossing — a planar graph is exactly a graph of genus 0, tying the combinatorial question of "can this graph be drawn flat" to the same handle-counting invariant that classifies [[Surface_(topology)|surfaces]]. **On the spine:** [[Graph_theory]] · [[Surface_(topology)]] · [[Manifold]]. ## Wikipedia : Wikitube **Strict pair:** [Wikipedia](https://en.wikipedia.org/wiki/Genus_(mathematics)) : [Wikitube](https://en.wikitube.io/wiki/Genus_(mathematics)) --- *Repopulated 2026-08-05 · existing three.js asset renamed + wired, Wikipedia-sourced overview · 0 deletions.*