# Simplex > [[PORTAL_Graph_theory|Graph theory]] spine. ## Microsims — three.js <div class="microsim-player"> <iframe src="https://wikitube-3d-microsims.netlify.app/Simplex_microsim.html" width="100%" height="520" frameborder="0" loading="lazy" sandbox="allow-scripts allow-same-origin" title="Simplex — three.js microsim"></iframe> </div> <p class="wt-pending"><strong>Note:</strong> staged, awaiting CDN deploy.</p> A simplex is the simplest possible polytope in any given number of dimensions: a point (0-simplex), a line segment (1-simplex), a triangle (2-simplex), a tetrahedron (3-simplex), and their higher-dimensional generalisations, each formed as the convex hull of one more point than the dimension requires. Simplices are the basic building blocks of simplicial complexes, the combinatorial structures used to approximate more complicated shapes. ## Overview This build renders simplices from zero through several dimensions (projected into 3D for anything above a tetrahedron) so the pattern — one more vertex, one more dimension — is visible directly. In [[Graph_theory|graph theory]] and combinatorics, a simplex corresponds to a complete graph: the 1-skeleton of an n-simplex (just its vertices and edges) is exactly the complete graph on n+1 vertices, every possible edge present, connecting the geometric and graph-theoretic pictures of "as connected as possible." **On the spine:** [[Graph_theory]] · [[Genus_(mathematics)]] · [[Manifold]]. ## Wikipedia : Wikitube **Strict pair:** [Wikipedia](https://en.wikipedia.org/wiki/Simplex) : [Wikitube](https://en.wikitube.io/wiki/Simplex) --- *Repopulated 2026-08-05 · existing three.js asset renamed + wired, Wikipedia-sourced overview · 0 deletions.*