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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.

 

BUT

 

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:

 

egg-diagonal.jpg

 

 

 

 The three lines together would give something like this:

 

 

 

 pifie-the-egg.jpg

 

 

 

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

 

 

universe-pifie.jpg 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

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