A toroidal moment can be generated spontaneously in inorganic (atom-based) ferrotoroidic materials that breaks both time-reversal and space-inversion symmetries, attracting great attention in solid-state chemistry and physics. In the field of molecular magnetism, it can also be achieved in lanthanide (Ln) involved metal-organic complexes usually with a wheel-shaped topological structure. Such complexes are called single-molecule toroics (SMTs), presenting unique advantages in spin chirality qubits and magnetoelectric coupling. However, to date, the synthetic strategies of SMTs have remained elusive, and the covalently bonded three-dimensional (3D) extended SMT has not hitherto been synthesized. Here, two luminescent Tb(iii)-calixarene aggregates with architectures of 1D chain (1) and 3D network (2) both containing the square Tb-4 unit have been prepared. Their SMT characteristics deriving from the toroidal arrangement of the local magnetic anisotropy axes of Tb(iii) ions in the Tb-4 unit have been investigated experimentally with the support of ab initio calculations. To the best of our knowledge, 2 is the first covalently bonded 3D SMT polymer. Remarkably, solvato-switching of SMT behavior has also been achieved for the first time by desolvation and solvation processes of 1.