Uploaded November 2010 | Updated September 2026, 2 weeks 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. 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 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. 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.)
