In Universe, planetary surface maps are represented as concentric rings of equal-area regions, or "environs". Each environ is approximately 16,000,000 km2 (1 600 ha) in area. (See my page on planet sizes.)
I hope to have diagrams soon which show the different environs for different sized planets. For now, imagine a circle of radius R, then another circle of radius 3R around that, then another of radius 5R, and so forth. The area between the R and 3R circles is divided into four equal parts; the area between 3R and 5R is divided into eight parts; then twelve, then sixteen, and so on. A size 0 world is a single radius R circle. A size 1 world is two of these representing two hemispheres. Size 2 worlds are one radius R map and one radius 3R map, for a total of 12 environs.
Now, we can see that, for worlds of size 2 or greater, the north and south polar regions can be represented by circular map projections. For worlds of size 2, 4, 6, or 8, the outermost ring of environs on the larger "hemisphere" is a cylindrical band. The rest of the environ rings can be represented as the base of a cone which intersects the planetary sphere at the latitude circles represented by the inner and outer boundaries of the ring.
If we assume that each ring is of equal width in latitude, and that the polar regions' radii are one-half of this width (an assumption that make sense looking at the maps), then we can calculate (from the maps and the calculate sizes of the planets) the dimensions of the circles, cylindrical bands, and conic bases; and we can then divide the bands and bases into equal-sized environs.
The results are the maps below. The per-hex scale is the same as the rectangular environ map in the book: one hex equals 100 km. Because of size limitations, there are ten hexes per inch, not five.
The maps are not complete; I'd like to add details such as: latitudes of boundaries; neighboring environ boundaries; fill-in blanks for environ number, predominant terrain type, and other features; and possibly hex numbering. But this is a start.
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