Three-dimensional (3D) periodic ordering of silicon (Si), an inorganic semiconductor, on the mesoscale was achieved by combining block copolymer (BCP) self-assembly (SA) based mesoporous alternating gyroidal network formation with nonequilibrium transient laser heating. 3D continuous and periodically ordered alternating gyroidal mesoporous carbon thin-film networks were prepared from spin coating, SA under solvent vapor annealing (SVA), and thermal processing of mixtures of a triblock terpolymer with resorcinol resols. The resulting mesoporous thin films, acting as structure-directing templates, were backfilled with amorphous silicon (a-Si). Nanosecond excimer laser heating led to transient Si melts conformally filling the template pores and subsequent Si crystallization. The ordered mesostructure of the organic polymer-derived templates was kept intact, despite being thermally unstable at the high temperatures around the Si melting point (MP), leading to high pattern transfer fidelity. As evidenced by a combination of grazing incidence small-angle X-ray scattering (GISAXS) and scanning electron microscopy (SEM), after template removal, the crystalline Si (c-Si) inherited the inverse network topology of the 3D mesoporous thin-film templates, but with reduced F222 space group symmetry (D2 point group symmetry) from compression of the cubic alternating gyroid lattice. Structures with this reduced symmetry have been proposed as photonic and phononic materials exhibiting topologically protected Weyl points, adding to the emerging field of BCP SA-directed quantum materials promising advanced physics and materials properties.