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3D printing is a process of making a three-dimensional solid object of virtually any shape from a digital model. Mathematica makes it possible to take complex algorithmically generated geometry and immediately output it for 3D printing--allowing the creation of physical 3D objects and models. Mathematica also provides broad support for importing arbitrary 3D scanning data for immediate analysis and visualization.

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Create a torus with a hexagonal mesh for 3D-printing

There is an explicit formula n = 30; m = 10; f[t_, u_] := {Cos[t] (3 + Cos[u]), Sin[t] (3 + Cos[u]), Sin[u]}; Graphics3D[Polygon /@ Table[ f[(4 π)/(3 n) (Cos[π k/3] + i 3/2), (2 π)/(Sqrt[3] m) (S …
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