# Hypercube > [[PORTAL_Cellular_automaton|Cellular automaton]] spine. ## Microsims — three.js <div class="microsim-player"> <iframe src="https://wikitube-3d-microsims.netlify.app/Hypercube_microsim.html" width="100%" height="520" frameborder="0" loading="lazy" sandbox="allow-scripts allow-same-origin" title="Hypercube — three.js microsim"></iframe> </div> <p class="wt-pending"><strong>Note:</strong> staged, awaiting CDN deploy — a Geometry-lane three.js asset, reused here since the hypercube is a tree-verified child of [[PORTAL_Cellular_automaton]].</p> A hypercube is the four-or-more-dimensional generalisation of the square and the cube: the n-dimensional analogue built by sweeping a cube through a new perpendicular direction. The four-dimensional case is called a tesseract, with 16 vertices, 32 edges, 24 square faces, and 8 cubic cells — a shape that cannot be embedded in three-dimensional space without distortion, which is why every 3D rendering of one is necessarily a projection. ## Overview Because a hypercube's true geometry lives outside the three dimensions available for viewing, every visualisation is a choice of projection, and different projections emphasise different structure — a perspective projection produces the familiar "cube within a cube" silhouette, while other projections preserve different symmetries instead. This build renders the shape as a live, rotatable 3D projection so the effect of viewing angle can be explored directly, the same projection technique that makes any n-dimensional structure, including a [[Cellular_automaton|cellular automaton]] lattice extended past two dimensions, viewable at all. The hypercube's edges also form a graph in which every vertex has exactly n neighbours — the same "closest cells" question a [[Von_Neumann_neighborhood|Von Neumann neighborhood]] answers for a cellular-automaton grid, just generalised to more dimensions than the grid itself uses. **On the spine:** [[Cellular_automaton]] · [[Von_Neumann_neighborhood]] · [[Elementary_cellular_automaton]] · [[Physics]]. ## Wikipedia : Wikitube **Strict pair:** [Wikipedia](https://en.wikipedia.org/wiki/Hypercube) : [Wikitube](https://en.wikitube.io/wiki/Hypercube) --- *Repopulated 2026-08-05 · existing three.js asset renamed + wired, Wikipedia-sourced overview · 0 deletions.*