We describe how varies the volume of tetrahedra, ditetrahedra, octahedra, and pyramids with a convex quadrilateral base following the displacement of each of their vertices according to a scalar multiple of the vector representing one of the coterminous edges at this vertex. Using different edges at a vertex generally leads to different transformed polyhedra. With the exception of tetrahedra, the volumes of the different polyhedra resulting from such transformations are different and not simple multiples of the volume of the original polyhedron. We also consider the limit case where the polyhedron becomes a finite and convex solid bounded by a regular surface.

transformations of convex polyhedra, volume of convex polyhedra.