I'm looking for a way to draw 3D surfaces in LaTeX with triangles on them to show the sum of angles being >, =, or < 180 degrees, exactly as in this photo

this photo http://i.space.com/images/i/000/036/078/original/universe-shape.jpg?1389843216.

I'd just like to do it myself, but I'm rather overwhelmed by the array of options available, and not sure where to start (nor how to do it). Thank you.

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    Of the tools often discussed here, then Asymptote is probably the most capable for 3D graphics. But perhaps you would prefer to draw this with a tool like Mathematica and generate a graphics file that you could include in your LaTeX document with graphicx package? Or even just include this picture? – Thruston Dec 30 '15 at 17:54
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    This might be of help: tex.stackexchange.com/questions/254820/… – John Kormylo Dec 30 '15 at 22:56

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