A New Deformation Family Of Schwarz' D Surface

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' 5-dimensional family. Nevertheless, o Delta meets classical deformations in a 1-parameter family on its boundary.