The 120-Cell is a regular 4-space figure, often described as the 4-D analog of the Dodecahedron. It is bounded by 120 dodecahedral cells, contains 720 pentagonal faces, 1200 edges, and 600 vertices. The 120-Cell is the dual of the 600-Cell. This particular 2-D projection is the most regular and has the fewest superimposed edges. The image shown here was produced by computer rotation of the figure in 4-space and projecting the edges orthogonally to the xy plane.
Finding the 120 dodecahedra that make up this figure is a little easier than finding the cells in a 600-cell. Still a little help is in order. The 600 vertices are arranged in 12 concentric rings. Starting at the outside and working in, the rings contain the following number of vertices respectively: 30, 60, 30, 60, 60, 60, 60, 60, 60, 30, 60 and 30. There are 30 each of the 4 different projections of the dodecahedral cells, shown below. It is interesting to note that each view has 2 faces that project as regular pentagons.
There are, of course, an infinite number of projections of this figure, 4 others are shown here. Another way to view this figure is a stereoscopic image of it's projection into 3-space.
Hyperspace24-Cell600-Cell
last revised: 9/28/02