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

Just as diving into water is to seek life's secrets, and immersion in water is to purify or be reborn, "crossing the waters is to effect a transformation from one state to another" (El Palacio, 1992).  If so, then what state has jurisdiction over the crossing of lakes Eerie and Ladoga?  Answer: Freedonia, under the rule of Rufus T. Firefly.

(Our image appears in The British Isles, translated from Nouvelle Géographie Universelle by Ernest Georg Ravenstein, 1887.)  

Ceylon (Sri Lanka) is a precursor to paisley.

Here's the track of the fox to the woods, from St. Nicholas magazine, 1903.

The year before Mr. Venn died, it was as if his diagrams hadn't made a dent.  Consider this muddled circle from Thinking: An Introduction to Its History and Science by Fred Casey, 1922.

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

Lawyer:  It would be enough to show that it [the Mediterranean] is in what — for the present purposes — can be deemed to be Scotland, and here we might usefully explore the possibility that Scotland, as we know it, may not always have occupied the precise position north of the border that it is commonly thought of as occupying today.  We are assisted here by the known fact that the general configuration of the Earth's surface, such as it is, was not arrived at overnight.  It is the end product of a not unlengthy process involving widespread upheaval over a period of several millennia, during the course of which things were in a considerable state of flux ... and it should not be difficult to demonstrate as an a priori possibility that Scotland — or what was subsequently to become known as Scotland — might, in one of the remoter periods of geological time, have occupied, however fleetingly, and prior to making its journey northwards to the position on the map that it has occupied ever since, [the Mediterranean].  If so, there would be a strong prima facie case for a reappraisal of the whole situation with a view to bringing the whole matter fairly and squarely within the jurisdiction of the Scottish courts....

Senior:  Sounds promising.

Minister:  Yes — I think one could give voice to a tentative eureka there.

[From Was He Anyone?, first performed in 1972]

An illustration from Napoléon et Son Temps by Roger Peyre (1896).

We enjoyed mapping out a fun Jonathan Caws-Elwitt bit.