Considerable interest in novel Si allotropes has led to intense investigation of tetrahedral framework structures during the last years. Recently, a guide to deriving sp3-Si allotropes from atom slabs of the diamond structure enabled a systematic deduction of several low-density modifications. Some of the Si networks were recognized as experimentally known frameworks, that is, so-called “chemi-inspired” structures. Herein we present nine novel Si networks obtained by modifying three-atom-thick slabs of a cubic diamond structure after smooth distortion by applying the same construction kit. Analysis of the structure–property relationships of these frameworks by using quantum-chemical methods shows that several of them possess direct bandgaps in the range suitable for light conversion. The construction kit was also applied to higher group 14 homologues Ge and Sn, and revealed interesting differences in the band structures and relative energies of the homologues. A new modification of Sn was identified as a poor metal, which denoted significant covalent-bond characteristics.