Polyconic projection class

Polyconic can refer either to a class of map projections or to a specific projection known less ambiguously as the American [polyconic projection]. Polyconic as a class refers to those projections whose parallels are all non-concentric circular arcs, except for a straight equator, and the centers of these circles lie along a central axis. This description applies to projections in equatorial aspect.

Polyconic projections

Some of the projections that fall into the polyconic class are:

American polyconic projection—each parallel becomes a circular arc having true scale, the same scale as the central meridian
Latitudinally equal-differential polyconic projection
Rectangular polyconic projection
Van der Grinten projection—projects entire earth into one circle; all meridians and parallels are arcs of circles.
Nicolosi globular projection—typically used to project a hemisphere into a circle; all meridians and parallels are arcs of circles.

A series of polyconic projections, each in a circle, was also presented by Hans Mauer in 1922, who also presented an equal-area polyconic in 1935. Another series by Georgiy Aleksandrovich Ginzburg appeared starting in 1949.
Most polyconic projections, when used to map the entire sphere, produce an "apple-shaped" map of the world.
There are many "apple-shaped" projections, almost all of them obscure.