  Consider an orthogonal polyhedron, i.e., a polyhedron where (at least after a
suitable rotation) all faces are perpendicular to a coordinate axis, and hence
all edges are parallel to a coordinate axis. Clearly, any facial angle and any
dihedral angle is a multiple of $\pi/2$.
  In this note we explore the converse: if the facial and/or dihedral angles
are all multiples of $\pi /2$, is the polyhedron necessarily orthogonal? The
case of facial angles was answered previously. In this note we show that if
both the facial and dihedral angles are multiples of $\pi /2$ then the
polyhedron is orthogonal (presuming connectivity), and we give examples to show
that the condition for dihedral angles alone does not suffice.
