Pair-of-pants surface

by dennedesigns Feb 1, 2016
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Thank you. I created them to illustrate a concept from topology: Any orientable surface of genus at least 2 may be decomposed into a sum of pairs of pants. Check out https://en.wikipedia.org/wiki/Pair_of_pants_(mathematics). These models were printed and displayed in the Fleet Science Center in San Diego, as part of the (now closed) Taping Shape exhibit there.

Its a pretty neat shape. In fact, somehow it seems that it should prove very useful in some context, but I'm not sure what. Its just a gut feeling. They're not exactly "The Wrong Trousers" :-) I would have been tempted to build this using OpenScad, boolean adding together a bunch of 30 degree torus sections and then boolean subtracting out paths similarly. The shape would not be quite the same. Nothing would be squarish, which may have been desirable here. It would be fun to make the legs half the size and generate an n level fractal with poly-trousers with 4, 8, 16, 32.... leg holes. Again, I'm not sure what one would do with such a manifold, but something may come to mind to someone. :-) Perhaps it would be enough for it to be fun to look at. Not everything has to have a utilitarian purpose. :-)