A Two-Sided Flat Earth Globe?
Fascinating "Flat-Globe" of the World, published in New York by the International Globe Company.
Includes a note that it was edited by Robert Peary, the American explorer and United States Navy officer who made several expeditions to the Arctic in the late 19th and early 20th centuries and is best known for claiming to have reached the geographic North Pole with his expedition on April 6, 1909.
The map was described in The Publishers Weekly, Volume 71, Part 2 (June 15, 1907), page 1836 as follows:
The International Globe Company, 115 Nassau Street, New York City, have brought out an educational apparatus of great value in their "International Flat Globe of the World," with its geographical history, edited by Commander Robert E. Peary. The globe is printed in eight colors on one flat disc, two feet four inches in diameter—the western hemisphere on one side and the eastern on the reverse of the disc—showing at a glance oceans, seas, lakes, mountains, international boundaries, colonial possessions, ocean currents, steamship routes, distances between ports, prevailing trade winds, latitude and longitude, cable routes, limits of ice drifts, railroad systems, and the longitudinal time at any point, east or west, by a series of clock faces.
The globe may be hung flat on the wall or laid flat on the table, and gives an unobstructed view of the earth's surface, and, being flexible, it can be rolled small so as to go in a trunk or valise. "The International Geographical History of the World," accompanying the globe, edited by Commander Peary, is a handy flexible book of 100 large pages, thoroughly indexed, and practically takes the place of a whole geographical library, because it gives the really important facts on geography in an instantly accessible form. It treats the subject under three heads: (1) Physical Geography, and the Phenomena and Forces of Nature; (2) Mathematical Geography, with Its Interesting Data; (3) National and Political Geography, which really embraces all the activities of the human race. It treats all these important subjects concisely, entertainingly, and with the very latest, up-to-date statistics and science. The globe and the accompanying book will be found as desirable and useful in the home and counting room as in school.
The "Flat-Globe" is apparently very rare. We located examples at the Library of Congress (copyright depository copy), University of Wisconsin, Milwaukee (likely the AGS/Peary copy) and 4 other examples in American and Canadian Libraries.
We find no record of another example at auction or in a dealer catalog.