Regular 4-polytope
Encyclopedia
In geometry
Geometry
Geometry arose as the field of knowledge dealing with spatial relationships. Geometry was one of the two fields of pre-modern mathematics, the other being the study of numbers ....

 a regular 4-polytope can mean either a convex or nonconvex (intersecting) 4-polytope.

See:
  • Convex regular 4-polytope
    Convex regular 4-polytope
    In mathematics, a convex regular 4-polytope is a 4-dimensional polytope that is both regular and convex. These are the four-dimensional analogs of the Platonic solids and the regular polygons ....

     - There are six convex regular polychora.
  • Schläfli-Hess polychoron - There are ten star (self-intersecting) regular star polychora.
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