This section deals with the Polyconic projection,
and projections related to it.
Sometimes, the term "Polyconic group" has been applied to any projection which is not obviously cylindrical, conic, or azimuthal, such as the Van der Grinten or Winkel's Tripel. However, as this illustration shows:
the Polyconic projection is an example of a basic scheme of projection, as fundamental as the cylindrical, conic, or azimuthal.
The blue line indicates the line (or point) of contact between the reducible surface to which the projection is made and the sphere. In the case of the Polyconic, this contact is along a great circle, so in a sense, the Polyconic can be thought of as a type of cylindrical projection.
Where it differs, however, is in the next step of the projection. A cylindrical projection next proceeds symmetrically along the meridians, as indicated by red lines, to place locations on the globe on the map. With the Polyconic, the red lines are parallels in the conventional case, so the scheme by which the globe as a whole is connected to the line of contact is different.
Note that the pseudocylindrical projections are created by starting with the blue line as a basis, using just one red line, and then changing the scale along the green lines from that red line. The same applies to the pseudoconic projections. However, Werner's projection is called pseudoconic instead of pseudoazimuthal; the term pseudoazimuthal has a completely different meaning.
One could imagine a class of pseudopolyconic projections derived from the same principle, but it would be of little use. Originally, I felt the distinguishing feature between the polyconic and pseudopolyconic should instead be whether or not the curvature of the parallels and the scale along the parallels varies in step, since this is the main property of the Polyconic.
Also, I think it is useful, even among the leftovers, to distinguish between the geometrically-based conventional projections, and the newer ones which are based on more general coordinate mathematics.