In geometry, the 24-cell (or icositetrachoron) is the convex regular 4-polytope, or polychoron, with Schläfli symbol {3,4,3}. It is also called an octaplex (short for "octahedral complex"), octacube, or polyoctahedron, being constructed of octahedral cells.
The boundary of the 24-cell is composed of 24 octahedral cells with six meeting at each vertex, and three at each edge. Together they have 96 triangular faces, 96 edges, and 24 vertices. The vertex figure is a cube. The 24-cell is self-dual. In fact, the 24-cell is the unique self-dual regular Euclidean polytope which is neither a polygon nor a simplex. Due to this singular property, it does not have a good analogue in 3 dimensions, but in 2 dimensions the hexagon, along with all regular polygons, are self-dual.
Read more about 24-cell: Constructions, Tessellations, Symmetries, Root Systems, and Tessellations, Quaternions, Projections, Three Coxeter Group Constructions, Visualization, Related 4-polytopes, Related Uniform Polytopes