Hyperbolic paraboloid. Draws straight "sticks" across two non-touching edges of tetrahedron to make paraboloid--set the # sticks to adjust resolution. Fewer sticks makes the geometry clearer. Use mouse to change direction of rotation.
Used framework of tetrahedron (faint red), drawing line from one edge of tetrahedron to opposing edge at regular increments. The two tetrahedron edges must be those that do not touch. Mathematicians are interested in it for several reasons. It has a "saddle surface" with a "doubly ruled surface" meaning you can line up straight sticks across one edge to another and also line up straight sticks across in the perpendicular direction and they all lie on this surface. As in any ruled surface, a line can be drawn through any point and the entire line stays on the surface. A few famous buildings use this design in their roofs. Such architecture distributes stress evenly and has an elegant appearance.
