High level G4MP2/G4 composite theoretical method thermochemical calculations were conducted on the parent tetrahedrane and cubane compounds and a suite of 20 mono-and polyfunctionalized derivatives with azo, nitro, and peroxo explosophoric substituents. The novel azo and peroxo derivatives of these Platonic solid hydrocarbons are likely to be local minima on their respective potential energy surfaces, suggesting these compounds may be priority synthetic targets. The high, mass normalized gas phase enthalpies of formation for both the tetrahedranes and cubanes exceed those of well-established primary (mercury fulminate and lead azide) and secondary (RDX and HMX) explosives by up to an order of magnitude. Other known (TNT, HMX, CL-20, octanitrocubane) or proposed (aminonitroalkanes and acetylenes, nitroboranes) high energy materials generally have substantially less favorable mass normalized gas phase enthalpies of decomposition than the most promising tetrahedrane or cubane derivatives presented herein.