Three novel low-dimensional open-germanates, denoted as SU-71, SU-72 and SU-73, were synthesized by solvothermal methods and their structures were determined by single crystal X-ray diffraction. The structures of SU-71, SU-72 and SU-73 are all built from Ge₇X₁₉ (X = O, OH or F) clusters that are connected according to the topologies related to the 4⁴ net. SU-71 has a layered structure following the 4⁴ net, SU-72 contains 2D slabs with unprecedented crescent-shaped 23-ring channels and SU-73 consists of zero-dimensional (0D) open nanoballs. SU-71 and SU-72 were both synthesized using 1-(2-aminoethyl)piperazine (AEP) as the organic structure directing agent, while pentaethylenehexamine (PEHA) was used for the synthesis of SU-73. All three phases form in the presence of HF, which promotes the formation of the Ge₇X₁₉ cluster. A comparison of the related structures reveals a relationship between the orientation of the Ge₇X₁₉ building units and the curvature of the 4⁴ net layer.