A new deformation family of Schwarz' D surface

We prove the existence of a new 2-parameter family o$Δ$ 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$Δ$ meets classical deformations in a 1-parameter family on its boundary.

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