Enantiopure alleno-acetylenic cage (AAC) receptors with a resorcin[4]arene scaffold, from which four homochiral alleno-acetylenes converge to shape a cavity closed by a four-fold OH-hydrogen-bonding array, form a highly ordered porous network in the solid state. They enable the complexation and co-crystallization of otherwise non-crystalline small molecules. This paper analyzes the axial conformers of monohalo- and (±)-trans-1,2-dihalocyclohexanes, bound in the interior cavity of the AACs, on the atomic level in the solid state and in solution, accompanied by accurate calculations. The dihedral angles ϑa,a (X-C(1)-C(2)-X/H) of the axial/diaxial conformers deviate substantially from 180°, down to 144°, accompanied by strong flattening of the ring dihedral angles. Structure optimization of the isolated guest molecules demonstrates that the non-covalent interactions with the host hardly affect the dihedral angles, validating that the host is an ideal means to study the elusive axial/diaxial conformers. X-ray co-crystal structures of AACs further allowed for a detailed investigation, both experimentally and theoretically, on the interplay between space occupancy, guest conformation, and chiral recognition based purely on dispersion forces and weak C-X···π (X = Cl, Br, I) and C-X···||| (acetylene) contacts (X = Cl, Br). The theoretical analysis of the non-covalent interactions between host and guest confirmed the high shape complementarity with fully enveloping dispersive interactions between the binding partners, rationalizing the high degree of enantioselectivity in the previously communicated complexation of (±)-trans-1,2-dimethylcyclohexane. This study also showed that (±)-trans-1,2-dihalocyclohexanes (X = Cl, Br) engage in significant halogen bonding (XB) interactions C-X···||| with the hosts. Slow host-guest exchange on the NMR time scale enabled the characterization of the encapsulated guests in solution, demonstrating that the complexes have identical geometries to those seen in the solid state, with the guests bound in axial/diaxial conformations.