Arno Peters was not the first person to come up with a map projection as an explicit critique of the Mercator projection (or at least its use as a general world map rather than as a navigation tool), nor was he the first to spend years proselytizing his creation. Bernard Cahill did the same thing beginning in 1909. His projection, the octohedral “butterfly map,” is the subject of this site run by Gene Keyes, who has spent no small effort of his own on the projection. The site contains a gallery of octahedral maps and Cahill’s 1909 article from The Scottish Geographical Magazine, in which he introduced the projection. That article is a must-read, if only for the account of how the 1908 San Francisco earthquake disrupted Cahill’s work and a critique of the Mercator projection that seems eerily contemporaneous. Thanks to peacay for the link.

See also Carlos Furuti’s page on polyhedral maps (see previous entry).