Van der Grinten Map Projection

http://www.progonos.com/furuti/MapProj/Normal/ProjOth/projOth.html
"Van der Grinten's proposals are examples of conventional designs, derived not from a perspective process but from an arbitrary geometric construction on the map plane. They are neither equal-area nor conformal (despite a superficial resemblance to projections by Lagrange, Eisenlohr and August), but intended to "look right", in the sense of conveying the notion of a round Earth (in this aspect, they resemble earlier globular projections) without departing too much from Mercator's familiar shapes."