A new deformation family of Schwarz' D surface

TL;DR

This paper introduces a new two-parameter family of embedded triply periodic minimal surfaces of genus 3, expanding the known classifications and properties of such surfaces beyond classical families.

Contribution

The authors prove the existence of a novel 2-parameter family of minimal surfaces that are distinct from known families, with unique properties and boundary relations.

Findings

Existence of a new 2-parameter family of surfaces

Surfaces share properties with classical deformations but are also exotic

Family intersects classical deformations in a 1-parameter boundary

Abstract

We prove the existence of a new 2-parameter family o$\Delta$ of embedded triply periodic minimal surfaces of genus 3. The new surfaces share many properties with classical orthorhombic deformations of Schwarz' D surface, but also exotic in many ways. In particular, they do not belong to Meeks' five-dimensional family. Nevertheless, o$\Delta$ meets classical deformations in a 1-parameter family on its boundary.