Costa surface

The Costa surface (a.k.a. the Hoffman-Meeks surface) is minimal surface. This means that it has the least possible surface area given its constraints and topology. Minimal surfaces are the sorts of surfaces that are formed by soap films. The Costa surface (technically, there is an infinite family of Costa surfaces...) is interesting because mathematicians had thought they knew all of the possible minimal surfaces, until this one was discovered in the 1980's. Understanding the geometry of these surfaces is a real challenge and was one of the early successes of computer-aided visualization. How much cooler is it that we can now print one and hold it in our hands?!