# Surface (topology) > [[PORTAL_Graph_theory|Graph theory]] spine. ## Microsims — three.js <div class="microsim-player"> <iframe src="https://wikitube-3d-microsims.netlify.app/Surface_topology_microsim.html" width="100%" height="520" frameborder="0" loading="lazy" sandbox="allow-scripts allow-same-origin" title="Surface (topology) — three.js microsim"></iframe> </div> <p class="wt-pending"><strong>Note:</strong> staged, awaiting CDN deploy.</p> In topology, a surface is a two-dimensional manifold: a shape where every point has a small neighbourhood that looks like a flat plane, even though the surface as a whole may be curved or closed up on itself, like a sphere or a torus. Surfaces can be defined as the boundary of a solid, as the graph of a function, or entirely abstractly, without reference to any surrounding space. ## Overview The classification theorem for closed surfaces is one of topology's cleanest results: every connected closed surface is either a sphere, a connected sum of tori, or a connected sum of projective planes, and its [[Genus_(mathematics)|genus]] together with orientability completely determines which one, up to continuous deformation. This build renders several standard surfaces — sphere, torus, and other configurable examples — so classification can be explored by direct manipulation. The same handle-counting genus that classifies a surface also bounds which [[Graph_theory|graphs]] can be drawn on it without edge crossings, tying this geometric classification to a purely combinatorial one. **On the spine:** [[Graph_theory]] · [[Genus_(mathematics)]] · [[Manifold]]. ## Wikipedia : Wikitube **Strict pair:** [Wikipedia](https://en.wikipedia.org/wiki/Surface_(topology)) : [Wikitube](https://en.wikitube.io/wiki/Surface_(topology)) --- *Repopulated 2026-08-05 · existing three.js asset renamed + wired, Wikipedia-sourced overview · 0 deletions.*