All possible pseudotetrahedral, stable polyhalocubanes were prepared, and their structures were proven by NMR spectroscopy and X-ray crystallography. Parity violating energy differences (DeltaEpv) and vibrational frequency shifts were computed. The DeltaEpv values are predicted to be one to two orders of magnitude smaller than those for the corresponding polyhalomethanes. However, the DeltaEpv energy ordering is the same as that for the methane analogues. For both substance classes, the (S) isomers are, with the exception of the bromochlorofluoroiodo derivatives, more stable than the (R) forms.