I have long casually assumed that the world Vornheim is on is cube-shaped. I figured: the whole planet is artificial and made of solid dungeon beneath a thin layer of vegetation, so of course it's a cube. That's about all I thought about that.
Then somebody--Stoya, I think--linked to this and I saw a few of the implications of a cube-earth.
One of the most interesting bits is: because the atmosphere would still radiate outward in a sphere from the planet's core, the habitable areas would be limited to non-communicating separate circular zones on each face of the planet.
In this set-up, the Medieval mind (and your non-curvature-adjusted gameworld map) is kinda right--the world is flat. You can literally walk to the edge of the (or, your) world, but before you did, you'd reach the edge of your atmosphere. However, if you could brave that, you could walk around the corner and reach another, entirely different biosphere.
(Note also that, depending on all kinds of physics, these other sides could have a similar or totally different climate.)
Now, obviously, in a pre-NASA civilization, the best way to get to these other biospheres would be to go through the earth and come out the other side. Bam, you're in a new world or--literally--on another plane of existence. And that's why they're called planes.
How did your FLAILSNAILS dwarf get from Vornheim to Greyhawk? Obviously he went straight down, took a right, and kept dungeoneering in that direction until he hit the surface.
Now this same exact set-up (non-communicating biospheres) could work with any radially symmetrical polyhedral world. i.e. Like a d20-shaped world could work like that. Easy...
So there you go: get from one plane to another with no Spelljamming, no magic (except all the physics-abuse it takes to make this basic shape plausible and a million other things I'm ignoring because I like this one single thing about the real physics), no Planescape, no portals, no fuss, no muss. All you need to do is find a dungeon with a sharp turn.
This explains why all the good stuff is down in the dungeons to begin with: that's where the trading happens. And, of course, why it's all so weird. Evolution took a different turn on face 8 than on face 9 due to the angle of the sunlight and all that...
It also makes it really easy to map an interplanar campaign. A few vertical geomorphs and 3d-maps and you can actually figure out where, in physical space, the DM put the other planes.