Uploaded November 2010 | Updated September 2026, 2 weeks 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. Edges in the hemisphere containing the camera are displayed as textured 3D tubes, whereas those in the hemisphere away from the camera are displayed as thin red lines.
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. Edges in the hemisphere containing the camera are displayed as textured 3D tubes, whereas those in the hemisphere away from the camera are displayed as thin red lines.
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.)
