Two series of wedge-shaped onium salts, one ammonium and the other phosphonium, having 3,4,5-tris(alkyloxy)benzyl moieties, exhibit thermotropic bicontinuous "gyroid" cubic (Cub(bi)) and hexagonal columnar liquid-crystalline (LC) phases by nanosegregation between ionophilic and ionophobic parts. The alkyl chain lengths on the cationic moieties, anion species, and alkyl chain lengths on the benzyl moieties have crucial effects on their thermotropic phase behavior. For example, triethyl-[3,4,5-tris(dodecyloxy)benzyl]ammonium hexafluorophosphate forms the thermotropic Ia (3) over bard Cub(bi) LC phase, whereas an analogous compound with trifluoromethanesulfonate anion shows no LC properties. Synchrotron small-angle diffraction intensities from the Ia (3) over bard Cub(bi) LC materials provide electron density maps in the bulk state. The resulting maps show convincingly that the Ia (3) over bard Cub(bi) structure is composed of three-dimensionally interconnected ion nanochannel networks surrounded by aliphatic domains. A novel differential mapping technique has been applied successfully. The map of triethyl-[3,4,5-tris(decyloxy)benzynammonium tetrafluoroborate has been subtracted from that of the analogous ammonium salt with hexafluorophosphate anion in the Ia (3) over bard Cub(bi) phases. The differential map shows that the counteranions are located in the core of the three-dimensionally interconnected nanochannel networks. Changing from trimethyl- via triethyl- to tripropylammonium cation changes the phase from columnar to Cub(bi) to no mesophase, respectively. This sensitivity to the widened shape for the narrow end of the molecule is explained successfully by the previously proposed semiquantitative geometric model based on the radial distribution of volume in wedge-shaped molecules. The LC onium salts dissolve lithium tetrafluoroborate without losing the Ia (3) over bard Cub(bi) LC phase. The Cub(bi) LC materials exhibit efficient ion-transporting behavior as a result of their 3D interconnected ion nanochannel networks. The Ia (3) over bard Cub(bi) LC material formed by triethyl-[3,4,5tris(decyloxy)benzyl]phosphonium tetrafluoroborate shows ionic conductivities higher than the analogous Ia (3) over bard Cub(bi) material based on ammonium salts. The present study indicates great potential of Cub(bi) LC nanostructures consisting of ionic molecules for development of transportation nanochannel materials.