What is a convex regular 4-polytope?
Q: What is a convex regular 4-polytope?
A: A convex regular 4-polytope is a 4-dimensional polytope that is both regular and convex.
Q: What are the analogs of convex regular 4-polytopes in three and two dimensions?
A: The analogs of convex regular 4-polytopes in three dimensions are the Platonic solids, while in two dimensions, they are the regular polygons.
Q: Who first described convex regular 4-polytopes?
A: The Swiss mathematician Ludwig Schläfli first described convex regular 4-polytopes in the mid-19th century.
Q: How many convex regular 4-polytopes are there?
A: There are precisely six convex regular 4-polytopes.
Q: What is the unique feature of the 24-cell polytope among the convex regular 4-polytopes?
A: The 24-cell polytope has no three-dimensional equivalent among the convex regular 4-polytopes.
Q: What are the 3-dimensional cells that bound each convex regular 4-polytope?
A: Each convex regular 4-polytope is bounded by a set of 3-dimensional cells that are all Platonic solids of the same type and size.
Q: How are the 3-dimensional cells fitted together in a convex regular 4-polytope?
A: The 3-dimensional cells are fitted together along their respective faces in a regular fashion in a convex regular 4-polytope.
