# 600-Cell 120-Cell Duality

600-Cell 120-Cell Duality

The 600-cell is the dual of the 120-cell. The 600 vertices of the 120-cell correspond to the 600 tetrahedra of the 120-cell and the 120 vertices of the 600-cell correspond to the 120 dodecahedra of the 120-cell. All the four-dimensional coordinates of both polytopes except their origins are divided by their norm to render them on the surface of a unit sphere in three dimensions. Select which subset of the coordinates is used for the three-dimensional rendering and adjust the size of the spheres to see edges. The 600 vertices and the 1200 edges of the 120-cell are red whereas the 120 vertices and 720 edges of the 600-cell are blue.