Editing 4-polytope (section)

==Geometry==
The convex [[regular 4-polytopes]] are the four-dimensional analogues of the [[Platonic solids]]. The most familiar 4-polytope is the [[tesseract]] or hypercube, the 4D analogue of the cube.

The convex regular 4-polytopes can be ordered by size as a measure of 4-dimensional content (hypervolume) for the same radius. Each greater polytope in the sequence is ''rounder'' than its predecessor, enclosing more content{{Sfn|Coxeter|1973|pp=292-293|loc=Table I(ii): The sixteen regular polytopes {''p,q,r''} in four dimensions|ps=: [An invaluable table providing all 20 metrics of each 4-polytope in edge length units. They must be algebraically converted to compare polytopes of unit radius.]}} within the same radius. The 4-simplex (5-cell) is the limit smallest case, and the 120-cell is the largest. Complexity (as measured by comparing [[Regular 4-polytope#As configurations|configuration matrices]] or simply the number of vertices) follows the same ordering.

{{Regular convex 4-polytopes}}