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To get the edges equal AND the angles 90/120/150 is not possible in 2D.


So we have to bend the lines.


I didn't get it work on a round sphere; it just doesn't fit.




when I use an egg-shape it should be possible!


I don't have the means and capabilities to make the calculations for it, so I just give the idea in drawings:


We bend the Pi-, e- and Phi-lines and with the diagonal we can calculate the edges.

Like this:






 The three lines together would give something like this:








 In a somewhat bigger picture you would get................




























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