I noticed that pentagons tile the projective plane (a spherical dodecahedron). Something they do not do on a flat euclidean plane.
Is there analogous 3D tilings (honeycombs) of a 3D projective hyperplane or 4D sphere (3-sphere)?
To put it a different way, the cube, octahedra, and tetrahedra are the only regular solid that fills 3D space. Does this situation change when we are working in a curved space?