[1] The prefix "hemi" is also used to refer to certain projective polyhedra, such as the hemi-cube, which are the image of a 2 to 1 map of a spherical polyhedron with central symmetry.
This is equivalent to demanding that the p/q-gons in the corresponding quasiregular polyhedra below can be alternatively given positive and negative orientations.
[3] In Magnus Wenninger's Dual Models, they are represented with intersecting prisms, each extending in both directions to the same vertex at infinity, in order to maintain symmetry.
The outward forms are: The hemipolyhedra occur in pairs as facetings of the quasiregular polyhedra with four faces at a vertex.
Since either m-gons or n-gons may be discarded, either of two hemipolyhedra may be derived from each quasiregular polyhedron, except for the octahedron as a tetratetrahedron, where m = n = 3 and the two facetings are congruent.