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A unique gyroid cubic phase has been discovered for a discotic star mesogen with three covalently attached DNA bases. In this cubic Ia3‾d ${Ia\bar{3}d}$ phase, the conjugated core of the mesogens and the thymine pseudo guests self‐assemble in mirror image continuous networks, representing a semiconducting material with three‐dimensional transport pathways. The hole carrier mobilities are found to be in the typical range of poly(phenylenevinylene) scaffolds. This structure is stabilized by a weak hydrogen bonding between the thymine bases and can be switched to a columnar liquid crystal – thermally and by the addition of complementary adenine guests. [ABSTRACT FROM AUTHOR]