There is a wide interest in three-dimensional (3D) photonic crystals that radically control the spontaneous emission of embedded quantum emitters and cavity QED, control thermal emission, allow for efficient miniature lasers, or efficient photoelectric conversion in solar cells [1,2]. Curiously, the experimental demonstration of a 3D photonic band gap remains a major challenge. To probe the band gap, spectra or dynamics are studied of emitters positioned inside the crystal, but such experiments are difficult for a number of practical reasons. On the other hand, a band gap is indicated by the overlap of stop bands seen in directional reflectivity or transmission experiments. A reflectivity peak (or transmission trough) may also occur due to other physical reasons. Hence experimentally observed stop bands are typically interpreted by comparing to band structures that, however, only pertain to infinite and perfect crystals. Thus there remains scope for a purely experimental probe of a 3D band gap, especially in view of the unavoidable deviations from perfect periodicity [3].