Uploaded November 2010 | Updated September 2026, 1 week ago
The 600-cell (hexacosichoron) is a 4-dimensional regular solid (with 120 vertices, 720 edges, 1200 triangular faces and 600 tetrahedral cells), which can also be considered as a tesselation of a 3-sphere by 600 regular tetrahedra. (This makes sense because the 3-sphere is positively curved: regular tetrahedra do not tile euclidean 3-space.) This video shows what it would look like to navigate this tesselation: the camera goes exactly once around the 3-sphere, following a great circle. Only the hemisphere centered around the camera is ever displayed, which explains why the edges seem to fade in a black fog when they get too far.
Technically, this was computed by performing a gnomonic projection, centered at the camera, of the polytope on 3-sphere. (And rotating the 3-sphere to "move" the camera.)
The 600-cell (hexacosichoron) is a 4-dimensional regular solid (with 120 vertices, 720 edges, 1200 triangular faces and 600 tetrahedral cells), which can also be considered as a tesselation of a 3-sphere by 600 regular tetrahedra. (This makes sense because the 3-sphere is positively curved: regular tetrahedra do not tile euclidean 3-space.) This video shows what it would look like to navigate this tesselation: the camera goes exactly once around the 3-sphere, following a great circle. Only the hemisphere centered around the camera is ever displayed, which explains why the edges seem to fade in a black fog when they get too far.
Technically, this was computed by performing a gnomonic projection, centered at the camera, of the polytope on 3-sphere. (And rotating the 3-sphere to "move" the camera.)
