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 Im3̄m cubic phase is always chiral, while the Ia3̄d 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 Ia3̄d phase the opposing chiralities of the two networks cancel, but not so in the three-networks Im3̄m phase. The high twist in the Im3̄m phase explains its previously unrecognized chirality, as well as the origin of this complex structure and the transitions between the different cubic phases.