The paper describes unexpected properties of hypercross-linked polystyrenes with ultimate cross-linking degrees of 300, 400, and 500%, where three, four, or five methylene links, respectively, could bind each polystyrene phenyl ring to its spacious neighbors. The polymers exhibit a strong electron spin resonance signal, unusual spectra in IR, UV, and visible ranges, and they are not typical dielectrics. The nonfunctionalized hypercross-linked polymers absorb significant amounts of inorganic acids, salts, and bases due to interactions of protons or other cations with electron-donating fragments of the aromatic network with the high extent of mutual connectivity and also due to dispersion interactions of anions with the polymer matrix.