Take the pole of each face of such a polyhedron with respect to a paraboloid of revolution, these poles will be the vertices of a second polyhedron whose edges are the conjugate lines of those of the former.
A polyhedron (A) is said to be the summital or facial holohedron of another (B) when the faces or vertices of A correspond to the edges of B, and the vertices or faces of A correspond to the vertices and faces together of B.
Octahedra having triangular faces other than equilateral occur as crystal forms. See Polyhedron and Crystallography.
If we take any polyhedron with plane faces, the null-planes of its vertices with respect to a given wrench will form another polyhedron, and the edges of the latter will be conjugate (in the above sense) to those of the former.
A polyhedron is said to be the hemihedral form of another polyhedron when its faces correspond to the alternate faces of the latter or holohedral form; consequently a hemihedral form has half the number of faces of the holohedral form.