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Tholian Web Question...

When I made my Tholian Web recreations, I came to the same conclusion. The web couldn't have been a sphere. I interpreted it as a cube and oriented it "standing on it's point." You can see and edge bend in the background in this image:

TholianWeb_zpsbea1ff98.jpg~original


As an exercise, I put the Enterprise directly in the center of the forming cube and looked to see how close I could get to the onscreen images with a carefully selected vantage point.
 
I always figured something along the lines of a D20 or D12

A D20 is an icosahedron, which is the shape they apparently did use in "In a Mirror, Darkly." A D12/dodecahedron is made of pentagonal faces, though, and I don't think there's any way to break those down into triangles.
 
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