You've heard that money makes the world go around, but it's actually bunny.  From The Bashful Earthquake by Oliver Herford (1899).

From Old Boston Taverns and Tavern Clubs, 1917.

Your instinct was correct -- our globe is all triangles.  From Monteith's Physical and Political Geography, 1875.

"Almost every world map you've looked at has been wrong," some say, but not this one from Chambers's Alternative Geography Readers, 1898.

The "four corners of the world" technically meet at the center, as we see in this diagram from Grundzüge der mathematischen Geographie und der Landkartenprojection by Anton Steinhauser, 1857.