Stepping back a bit and taking a gander at the big picture:

The world maps of the future are probably going to look a lot more like these than like an artfully positioned Oblique Mercator projection. At least when you’ve got ocean matters on your mind.
FYI: if you’re into analog swag, these maps are sized to mount back-to-back.
Map edges are continental divides of Africa, Asia, and Europe.
Relative sizes of watersheds around the map edge are directly comparable.
Inland basins attach at their lowest spout.
Relative sizes and internal proportions of oceans and seas are roughly accurate.
Many of the long-distance flights the Nautilus Live crew are talking about can be followed on this map.
Here’s the map in near-maximum resolution. (Click on map for full-size version)
(You might have to open it in a photo-editing software such as Photoshop. I have trouble opening this in Mac Preview.)
(Not sure if this will work; it’s the largest file I’ve yet posted.)
(Yeah. Doesn’t want to open on screen. Try right-clicking on the map and select “download linked file.”)
Suggestions welcome for how to fix this posting glitch. EDIT: the download problem appears to be native to my home computer. Enjoy the map!
I had to make up the projection. Long story. Summary is that the cut (the edge of the map) is 270˚ (three-fourths of a circle).
The purpose was to put the tiger stripes, the south polar district, into global context. Other compact maps were either unable to make the polar region large enough, relative to the nether regions, or the map periphery went squirrelly.
The cut can turn on 45˚ increments, which has the effect of rotating the stripes around the pole; the lobes refocus from leading and trailing hemispheres (the posted map) to anti- and sub-Saturnian hemispheres.
A really large version is in the works. Maybe by March, knock on wood.
Here’s what the grid looks like:
with a little Photoshopping, you could make your own! Hmm . . . would this projection be of any use on another planet or moon?
My design for an children’s participatory exhibit titled Spaces & Illusions, which was installed from 1976–1980, give or take a few months, at Atlanta’s High Museum of Art.
Its appearance here in a blog about a novel way to make world maps may appear incongruous until I offer that the process of designing and installing the exhibit presaged all the constant-scale natural boundary maps you find here.
Presaged in a cluelessly groping way, I admit, but some things take time to resolve themselves.
This image copyright Chuck Clark 2012, all rights reserved.