Gas-phase standard state (298.15 K, 1 atm) enthalpies of formation (ΔfH(g)o) and enthalpies (ΔacidH(g)o) and free energies (ΔacidG(g)o) of acid dissociation were calculated for the [m, n]polyprismanes (m ≥ 2; n = 3–8; m × n ≤ 16) using the composite method CBS-Q//B3, G4MP2, and G4 levels of theory. Excellent agreement was obtained between the theoretical estimates and experimental values for [2, 4]polyprismane (cubane), the only member with reliable experimental data. Gas-phase acidities of the [2, 3], [2, 4], and [2, 5]polyprismanes correlate well with percent s-character of the C–H bonds as determined by nuclear magnetic resonance spectroscopy. Based on this correlation, and calculations on the [2, n] (n = 3–8) series, no substantial change in the gas-phase acidity or C–H bond s-character is expected with increasing [2,n]polyprismane ring size at n = 6–8. Where three or more stacked [m, n]polyprismane rings are present (m > 2), geometry optimizations for the deprotonated anions converged on cage-opened non-prismatic geometries, suggesting these compounds may be structurally unstable to gas-phase deprotonation/protonation cycles and potentially preventing reliable experimental measurement or calculation of their acidities. Total strain energies (Estr) increase with larger [m, n]polyprismane size, and strain energies per one C–C bond (EstrCC) increase with increasing stack height within a given ring size series. Within a given stack height, EstrCC reaches a minimum with a ring size of five, increasing with either decreasing or increasing ring size away from this minima. Estr and EstrCC do not correlate with gas-phase acidity, likely because the deprotonated anionic [2, n]polyprismane geometry retains approximately equal strain as the undissociated species despite substantial geometry changes due to carbon acid dissociation.