Rectangle to Octahedron, Octahedron to Sphere

I'm embarassed to admit that I just want to world-build and here I am, back at the quick and dirty end of things, which is bunch of boxes, essentially a schematic mapped to a rectangular world map. What I can do is rough out the land and sea area, simple hydrographic ratio, although this should be a height map paired with an inventory of water.
I'm going to use an octagon, but I'm going to do it a little differently from what you might expect; instead of eight triangles paired up at the equator and meeting at the poles, we have two squares side by side, forming a rectangle. Each square is actually four triangles poking up and out of the 2d map to form the near and far poles of an octahedron. There will be distortions of course, and I could use a cube to have less distortion, but this is not worth the aggravation. The rectangular map can actually be considered a bunch of quads rather than triangles, especially after I spherify the octahedron. The resolution can be very coarse, 8 by 4 for example, or as fine as 520 by 260 in this case, where my canvas is 520 by 260 pixels. Or, 26 by 13 for over three hundred 20 pixel rectangles and quads. Eight hundred 13 pixel quads, 40 by 20, is probably more reasonable, and two hundred 26 pixel quads would mean each is ~1/2% of the surface.