Dynamic Mirror-Symmetry Breaking in Bicontinuous Cubic Phases**

Chiral segregation of enantiomers or chiral conformers of achiral molecules during self-assembly in well-ordered crystalline superstructures has fascinated chemists since Pasteur. Here we report spontaneous mirror-symmetry breaking in cubic phases formed by achiral multichain-terminated diphenyl-2,2′-bithiophenes. It was found that stochastic symmetry breaking is a general phenomenon observed in bicontinuous cubic liquid crystal phases of achiral rod-like compounds. In all compounds studied the ${{\it Im}\bar 3m}$[Image: see text] cubic phase is always chiral, while the ${Ia\bar 3d}$[Image: see text] phase is achiral. These intriguing observations are explained by propagation of homochiral helical twist across the entire networks through helix matching at network junctions. In the ${Ia\bar 3d}$[Image: see text] phase the opposing chiralities of the two networks cancel, but not so in the three-networks ${{\it Im}\bar 3m}$[Image: see text] phase. The high twist in the ${{\it Im}\bar 3m}$[Image: see text] phase explains its previously unrecognized chirality, as well as the origin of this complex structure and the transitions between the different cubic phases.