Hello,
If you want to create a hyperbolic polyhedron in three.js, I have a method. Examples:
I explain the method on my blog, here; I provide the code for a couple of languages. See this Github repo for the Python way.
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It looks nice.
If you add grid lines over the surfaces this might make it easier to perceive their shape.
Not sure because there is a lot of triangles. Another material would make it easier I think.
Yes, showing all triangles will not be good, but what about just a few lines that make the shape easier to see? Something like the lines in these figures:
