One the best uses of computer-controlled manufacturing tools, e.g., 3D printing, are to create shapes that you have to touch to believe; a visualization on a flat screen is not enough.
Minimal surfaces, such as the Costa surface and the Helicoid with hole (or handle), are one large class: stick your fingers through the holes to understand where and how they connect.
I remember finding it hard to believe that a hyperbolic paraboloid is a ruled surface. And that the Kelvin cell and Weaire-Phelan cell are curved.
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