As noted in the first page of this chapter, I feel that this projection stands almost in a class by itself.
It can be, easily enough, dismissed as merely a conventional projection which serves as an easy-to-construct substitute for the transverse case of the Plate Carrée (Cassini's Projection). And indeed, that basically is its main usefulness.
However, the fact that it preserves the correct curvature for the representation of each parallel seems to me as worthy of a specific classification as the characteristics which identify azimuthal, cylindrical, and pseudocylindrical projections.
Also, the Polyconic seems to have a particular appeal to the eye, perhaps deriving from the true curvature of each parallel. Thus, star maps have been constructed with a similar layout to that of the world map above. Also, it is often used for making the gores from which globes are constructed. (The illustration here uses gores too wide for constructing a proper globe; gores of half this width are in common use for that purpose.)