There are seven topologically distinct convex hexahedra,[1] one of which exists in two mirror image forms.
Additional non-convex hexahedra exist, with their number depending on how polyhedra are defined.
Two polyhedra are "topologically distinct" if they have intrinsically different arrangements of faces and vertices, such that it is impossible to distort one into the other simply by changing the lengths of edges or the angles between edges or faces.
There are seven topologically distinct convex hexahedra,[1] the cuboid and six others, which are depicted below.
Three further topologically distinct hexahedra can only be realised as concave acoptic polyhedra.