Uploaded November 2010 | Updated September 2026, 1 week ago
The 120-cell (hecatonicosachoron) is a 4-dimensional regular solid (with 600 vertices, 1200 edges, 720 pentagonal faces and 120 dodecahedral cells), which can also be considered as a tesselation of a 3-sphere by 120 regular dodecahedra. (This makes sense because the 3-sphere is positively curved: regular dodecahedra 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 120-cell (hecatonicosachoron) is a 4-dimensional regular solid (with 600 vertices, 1200 edges, 720 pentagonal faces and 120 dodecahedral cells), which can also be considered as a tesselation of a 3-sphere by 120 regular dodecahedra. (This makes sense because the 3-sphere is positively curved: regular dodecahedra 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.)
