In geometry, a polychoron or 4-polytope is a four-dimensional polytope.

In four dimensional geometry, a 16-cell or hexadecachoron is a regular convex 4-polytope.

The convex hull of these 24 elements in 4-dimensional space form a convex regular 4-polytope called the 24-cell.

Each convex regular 4-polytope is bounded by a set of 3-dimensional cells which are all Platonic solids of the same type and size.

The two-dimensional analogue of a 4-polytope is a polygon, and the three-dimensional analogue is a polyhedron.

Each group is specified as a Coxeter group, and like the polyhedral groups of 3D, it can be named by its related convex regular 4-polytope.

In four-dimensional geometry a regular polychoron can mean either a convex or nonconvex (intersecting) polychoron (4-polytope).

In mathematics, a convex regular 4-polytope (or polychoron) is 4-dimensional polytope which is both regular and convex.

In geometry, a uniform polychoron (plural: uniform polychora) is a polychoron (4-polytope) which is vertex-transitive and whose cells are uniform polyhedra.

T. Gosset: On the Regular and Semi-Regular Figures in Space of n Dimensions, Messenger of Mathematics, Macmillan, 1900 (3 regular and one semiregular 4-polytope)

In a polyhedron, an edge can also be considered a ridge, being the shared boundary between two faces, and in a 4-polytope, an edge can be considered a peak, with a cycle of 3 or more faces and cells wrapping around it.