Ab initio polarization configuration interaction (POL‐CI) calculations show that Ne+3 and Ar+3 are both linear, in agreement with indirect experimental evidence on Ar+3 and in contradiction to earlier approximate theoretical calculations on Ar+3, which predicted an equilateral triangular geometry. The experimentally unknown Ne+3 dissociation energy is predicted to be 0.15±0.01 eV. Simple diatomics‐in‐molecules (DIM) calculations were shown to be in very good agreement with the ab initio results. DIM calculations predict that Kr+3 and Xe+3 are also linear. All the rare‐gas–trimer ions possess at least one very strong absorption band in the visible, even stronger than the near ultraviolet absorption band of the rare‐gas–dimer ions.