Orthogonal polyhedron

An orthogonal polyhedron is a polyhedron in which all edges are parallel to the axes of a Cartesian coordinate system,[1] resulting in the orthogonal faces and implying the dihedral angle between faces are right angles.

The angle between Jessen's icosahedron's faces is right, but the edges are not axis-parallel, which is not an orthogonal polyhedron.

[2] Polycubes are a special case of orthogonal polyhedra that can be decomposed into identical cubes and are three-dimensional analogs of planar polyominoes.

This showed the requirements for the polyhedral equivalence conditions by Dehn invariant.

[5][2] Orthogonal polyhedra may also be used in computational geometry, where their constrained structure has enabled advances in problems unsolved for arbitrary polyhedra, for example, unfolding the surface of a polyhedron to a polygonal net.