The family of materials RE4TGe8 (RE = Yb, Gd; T = transition metal) exhibits directional zero thermal expansion (ZTE) via a process that is associated with the linking of planar square nets in the third dimension. The Ge square nets in these compounds exhibit commensurate long-range modulations similar to those observed in charge-density-wave compounds. The ZTE is manifested in the plane of the square nets from 10 to 300 K with negligible volume expansion below similar to 160 K. The specific atomic arrangement in RE4TGe8 enables a Poisson-like mechanism that allows the structure to contract along one direction as it expands only slightly in the perpendicular direction.