Polychoron

4-simplex (5-cell)	4-orthoplex (16-cell)	4-cube (Tesseract)
24-cell	120-cell	600-cell
Graphs of six convex regular 4-polytope.

In geometry, a polychoron (plural: polychora) is a figure in four dimensions. The word comes from Greek poly, which means many and choros which means room, or space. Sometimes the figure is called 4-polytope or polyhedroid. The analogue figure in two dimensions is a polygon, and the one in three dimensions is a polyhedron.

The tesseract is the best known polychoron, containing eight cubic cells, three around each edge.It is viewed here as a Schlegel diagram projection into 3-space, distorting the regularity, but keeping its topological continuity. The eighth cell projects into the volume of space exterior to the boundary.

Other websites

• Eric W. Weisstein, Polychoron at MathWorld.
• Four dimensional figures page
• Jonathan Bowers: Uniform polychora