Chiral symmetry breaking in soft matter is a hot topic of current research. Recently, such a phenomenon was found in a fluidic phase showing orientational order of molecules-the nematic phase; although built of achiral molecules, the phase can exhibit structural chirality-average molecular direction follows a short-pitch helix. Here, we report a series of achiral asymmetric dimers with an odd number of atoms in the spacer, which form twisted structures in nematic as well as in lamellar phases. The tight pitch heliconical nematic (NTB) phase and heliconical tilted smectic C (SmCTB) phase are formed. The formation of a variety of helical structures is accompanied by a gradual freezing of molecular rotation. In the lowest temperature smectic phase, HexI, the twist is expressed through the formation of hierarchical structure: nanoscale helices and mesoscopic helical filaments. The short-pitch helical structure in the smectic phases is confirmed by resonant X-ray measurements.