Let us define a pyramid as a convex polyhedron with one quadrilateral face and four triangular faces.

Question: How many pyramids (or families of pyramids) are known that can fill 3D space without gaps? The packing need not be face to face or edge to edge (not sure if these relaxations matter at all).

Remark: the same question on tetrahedrons is not fully resolved as explained in https://www.jstor.org/stable/2689983