Le_Forgeron wrote:

> Using a mercator projection (100% spherical projection), but not as
> usual (instead of a point on equator for center, using the south pole,
> and forget about Greenwich meridian, off by 60°)

I think this is a transverse Mercator projection (Lambert 1772)
for a specific choice of central meridian (the usual representation
seems to be shifted 25% with respect to yours, though, i.e. poles
at 25% and 75% and equator at center and border).

http://en.wikipedia.org/wiki/Transverse_Mercator_projection

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