The 600-Cell is a regular 4-space figure, often described as the 4-D analog of the Icosahedron. It is bounded by 600 tetrahedral cells, contains 1200 triangular faces, 720 edges, and 120 vertices. This particular 2-D projection is the most regular and has the fewest superimposed edges. This figure is the dual of the 120-Cell. This projection was used by Coxeter as the frontispiece for his book Regular Polytopes. The image shown here was produced by computer rotation of the figure in 4-space and projecting the edges to the xy plane.
600-Cell
Perceiving this figure can be a challenge! I will take a simple visual approach. The 120 vertices are arranged in 4 rings of 30 vertices each. Each of the groups of 30 are regularly spaced. There are 12 different projections of the tetrahedral cells. They are shown in the figure below. The number of times each projection is repeated is displayed either inside or near the figure. The projections with 60 repetitions are divided into 2 groups of 30. There are 30 as shown and another 30 that are mirror images of the ones shown. Color is used only to differentiate between the tetrahedra that are superimposed.
600-Cell with tetradedra highlighted
If your not worn out yet, there is also a stereoscopic view of a 3-D projection of this figure, or check out some other 600-Cell projections.
Hyperspace120-CellHyperspace
last revised: 9/28/02