A set of new porous materials, namely zeolite nanocage schwarzite-like crystals with the elements of both nanotubes and fullerenes in the structure is proposed as a result of ab initio and density-functional theory calculations. Twelve new Extradiamond phases of boron nitride, carbon, silicon and silicon carbide are calculated as three different hybridized crystals. The details of recently synthesized Explosion-BN (E-BN) phase are highlighted for the first time with electronic structure and vibrational frequency analysis. E-BN is supposed to be sp (2)/sp (3)-hybridized FAU-zeolite structure with calculated unit cell of 12.177 and a band gap of 3.2 eV. Calculated IR bands for E-BN120 cluster and observed experimentally E-BN absorption spectrum are well-correlated with appropriate IR spectra of FAU-zeolite. Armchair and zig-zag nanotubes are classified as (n,n,k) and (n,0,k), respectively, where k is the number of hexagons along the nanotube axis. Novel materials are proposed as (n,m,k)-FTC, where FTC stands for framework type code. We also indicate the possibility of creation of filled hybrid networks of different segment lengths, radii and compositions for thermoelectric and novel device applications.