We report on the fabrication and characterization of void-based body-centered-cubic (bcc) photonic crystals in a solidified transparent polymer by the use of a femtosecond laser-driven microexplosion method. The change in the refractive index in the region surrounding the void dots that form the bcc structures is verified by presenting confocal microscope images, and the bandgap properties are characterized by using a Fourier transform infrared spectrometer. The effect of the angle of incidence on the photonic bandgaps is also studied. We observe multiple stop gaps with a suppression rate of the main gap of 47% for a bcc structure with a lattice constant of 2.77 μm, where the first and second stop gaps are located at 3.7 μm and 2.2 μm, respectively. We also present a theoretical approach to characterize the refractive index of the material for calculating the bandgap spectra, and confirm that the wavelengths of the observed bandgaps are in good correlation with the analytical predictions.