Mathematician, Artist, Teacher, Maker, I work to corrupt people into mathematical thinking and experiences through toys, coloring images, and more. We do so much work to show that mathematics is worthy and useful (as it is), but less to show the deep sense of joy and play that inspires so many mathematicians in their work. I believe mathematical art and toys are paths into maths that can both lead to deep ideas and motivate the rigorous study required to capture them.
Curvahedra is not a single artwork but a system to make all sorts of possible objects. The individual pieces link together to create a surface and form is created by controlling the local Gaussian curvature using the Gauss-Bonnet theorem, though you do not need to know that to do it. Just start connecting and see what you come up with!
Three designs showing patterns that can be obtained running a CNC mill along lines. For the first two pieces the lines are defined purely mathematically. For the third the lines are inspired by the geometry of the wood itself, always lying at right angles to the grain.
The pseudosphere is a surface of constant negative curvature. In other words, it is a saddle at every point, and they are all equally "saddle-y" (to a particular definition of "saddle-y"). This model shows what "straight lines" look like on this surface, the lines which cannot be made shorter with local wiggles.