Quantum chemical computations show that three groups of inorganic ions and neutral molecules, whose structures have long been known and characterized, are aromatic due to through-space homoconjugation: (i) I-4(2+), S6N42+, and S2I42+ dications and the (O-2)(4) cluster with pericyclic transition-state-like (PTS-like) homoaromaticity; (ii) the bishomoaromatic Te-6(2+) and 1,5-diphosphadithiatetrazocines; and (iii) the spherically homoaromatic Te-6(4+). The S2I42+ dication has an unusually high S-S bond order (similar to 2.3) and dual PTS-like aromaticity arising from two separate sets of four-center, six-electron (4c-6e) in-plane through-space conjugation. The diamagnetic (O-2)(4) structural unit recently observed in epsilon-phase oxygen solid has quadruple PTS-like aromaticity, each arising from 4c-6e in-plane through-space conjugation within an O-2-O-2 plane. Finally, we note that the lighter S-6(4+) and Se-6(4+) homologues of Te-6(4+) also are spherically homoaromatic and might be observable in complexes.