| A polytope is a geometric object with flat sides in any number of dimensions. In two dimensions, polytopes are polygons. In three dimensions, they are polyhedra. In four dimensions, they are called polychora or 4-polytopes. The 600-cell is a regular 4-polytope with 120 vertices, 720 edges, 1200 triangular faces, and 600 tetrahedral cells. It is the four-dimensional analog of the icosahedron. The 600-cell has the H4 symmetry group, which contains 14400 elements. This is the largest finite reflection group in four dimensions. The vertices of the 600-cell can be expressed using the golden ratio phi. The coordinates include values like phi over two and one over two phi. The 600-cell is dual to the 120-cell, which has 600 vertices. Together they form the most symmetric structures possible in four dimensions. |