My dream map projection

I want a world map that’s… uh…

1. Take a polyhedral projection, like octahedral or icosahedral (or even more faces, the more faces the better, it doesn’t have to be a platonic solid).
2. Unfold. You now have something that looks like the Dymaxion or Butterfly.
3. But rotate the continents so they look like they’re placed in traditional world maps. Careful: do not cut every li’l face, just cut out the continents, as big pieces as possible, and rotate them and place them.
4. Add water! It’s not a sea map, it’s fine if oceans are distorted, it’s a land map! Add more sea! Make some sea distances smaller and some larger, just add endless distortion out at sea.

Basically take a rectangle, fill it with water, cut out the continents from a Dymaxion style map (making few big cuts rather than many small cuts), place them in that water guided by some other projection.

So the map still looks rectangular and “normal” except it doesn’t have Mercator’s follies.

That’s the world map poster I’d want. I don’t want it to look like an orange peel but I want the projection properties of an orange peel map. I’ve wanted this since 1988 when I first saw the Goode homolosine, which isn’t a polyhedral projection but it’s what inspired the idea: “why not just place this on a backdrop of sea so it looks normal!?”

(And then do the opposite for a separate map that is a sea map at the expense of land accuracy.)

This sort of map, like all polyhedral projection maps, is pretty useless for actually measuring things on. It’s just nice to look at and we get to see places in their real sizes (as long as they’re land places and not oceans). The Thissots indicatrix is awesome on this one.♥︎

A few years ago the build the earth project for Minecraft had a similar idea calling it “Modified Airocean”. Very awesome! I haven’t found images but judging from the text description, it sounds right:

This map projection provides an extremely low amount of distortion of both shapes and sizes on land, at the cost of heavily distorting the oceans. Unlike the Dymaxion, Modified Airocean is not intended to be unfolded into a 3D object like an icosahedron, and has its continents placed such that it looks somewhat similar to an equirectangular projection.

But I wanna see big poster maps based on this! I can’t even find any dinky li’l low-rez JPEGs of what they had, let alone a huge wall map.

My folks used to have a big canvas world map (from Ikea I think) but it looked so distorted since it was Mercator. That was only the second biggest problem; the biggest issue was that it used Copperplate Gothic.