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area accurate Peters projection
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Please no. Peters was very good in selling the very old and very awful equal area cylindrical as a new politcal correct idea. There do exist tons of equal area projections, they simply are not cylindrical.
IMHO it is much more important that a map looks good than that it is exactly equal area. If you would accept a flat map you could go for a nice sinusoidal projection. Or half the earth and take some polar projection.
That distances are too much different at different latitudes is really a problem with the too much used Mercator projection.
Using hexagons with just 12 pentagons is enough to get a nice computerized map, but in game terms that means that there are 12 special points with less neighbours, these artifical problems will play a mayor role in tactics so that is not the way to go.
A way with squares would be to make a nice projection of the earth on a cube (I saw once the formula's in some book in our library) and glue them programmatically to each other. When there will be the eight corners of the cube who will have some special role, but everything else can stay the same. and all squares will have the same number of neighbours.
Only real problem for a company like firaxis would be to redo the shortest path routines.