Editing List of mathematical shapes (section)

=== Four-dimensional regular polytopes ===
*convex [[regular 4-polytope]]
**[[5-cell]], the 4-space [[Simplex]]
**[[8-cell]], the 4-space [[Hypercube]]
**[[16-cell]], the 4-space [[Cross-polytope]]
**[[24-cell]]
**[[120-cell]]
**[[600-cell]]

==== Degenerate (spherical) ====
*[[Ditope]]
*[[Hosotope]]
*[[3-sphere]]

====Non-convex====
*Star or (Schläfli–Hess) [[regular 4-polytope]]
**[[Icosahedral 120-cell]]
**[[Small stellated 120-cell]]
**[[Great 120-cell]]
**[[Grand 120-cell]]
**[[Great stellated 120-cell]]
**[[Grand stellated 120-cell]]
**[[Great grand 120-cell]]
**[[Great icosahedral 120-cell]]
**[[Grand 600-cell]]
**[[Great grand stellated 120-cell]]

====Tessellations of Euclidean 3-space====
*[[Honeycomb (geometry)|Honeycomb]]
*[[Cubic honeycomb]]

====Degenerate tessellations of Euclidean 3-space====
*[[Hosohedron]]
*[[Dihedron]]
*[[Order-2 apeirogonal tiling]]
*[[Apeirogonal hosohedron]]
*[[Order-4 square hosohedral honeycomb]]
*[[Order-6 triangular hosohedral honeycomb]]
*[[Hexagonal hosohedral honeycomb]]{{Citation needed|reason=See Talk: Placing 'mathematical shapes' that do not have a wikipedia article|date=April 2018}}
*[[Order-2 square tiling honeycomb]]
*[[Order-2 triangular tiling honeycomb]]
*[[Order-2 hexagonal tiling honeycomb]]

====Tessellations of hyperbolic 3-space====
*[[Order-4 dodecahedral honeycomb]]
*[[Order-5 dodecahedral honeycomb]]
*[[Order-5 cubic honeycomb]]
*[[Icosahedral honeycomb]]
*[[Order-3 icosahedral honeycomb]]
*[[Order-4 octahedral honeycomb]]
*[[Triangular tiling honeycomb]]
*[[Square tiling honeycomb]]
*[[Order-4 square tiling honeycomb]]
*[[Order-6 tetrahedral honeycomb]]
*[[Order-6 cubic honeycomb]]
*[[Order-6 dodecahedral honeycomb]]
*[[Hexagonal tiling honeycomb]]
*[[Order-4 hexagonal tiling honeycomb]]
*[[Order-5 hexagonal tiling honeycomb]]
*[[Order-6 hexagonal tiling honeycomb]]