Triply Periodic Surfaces

There is a large number of known embedded triply periodic minimal surfaces. Moreover, it seems that the examples come in 5-dimensional families, most of which are only partially understood. Our lack of knowledge of these surfaces makes it very hard to put them into categories. For the moment, we use the genus of the quotient by the largest lattice of orienation preserving translations as a guide.

However, a large class of classical and semi-classical surfaces have a sufficiently simple description that allows us to put them into series of increasing complexity.

• genus 3
• genus 4
• genus 5
• higher genus
• Surfaces in right prisms (new)