The detection of two similar periodicities (3001 and 3028 s) in the light curve of V1405 Aq1, a low mass X-ray binary (LMXRB), has attracted the attention of many observers. Two basic competing models have been offered for this system. According to the first, V1405 Aq1 is a triple system. The second model invokes the presence of an accretion disc that precesses in the apsidal plane, suggesting that the shorter period is the orbital period while the longer is a positive superhump. The debate on the nature of V1405 Aq1 has been continued until very recently. Re-examination of previously published X-ray data reveals an additional periodicity of 2979 s, which is naturally interpreted as a negative superhump. The recently found 4.8-d period is consequently understood as the nodal precession of the disc. This is the first firm detection of negative superhumps and nodal precession in a LMXRB. Our results thus confirm the classification of V1405 Aq1 as a permanent superhump system. The 14-yr argument on the nature of this intriguing object has thus finally come to an end. We find that the ratio between the negative superhump deficit (over the orbital period) and the positive superhump excess is a function of orbital period in systems that show both types of superhumps. This relation presents some challenge to theory as it fits binaries with different components. We propose that a thickening in the disc rim, which causes increased occultation of the X-ray source, is the mechanism responsible for both types of superhumps in LMXRBs. However, the positive signal is related only to the pronounced dips in the light curve, where the point-like central source is covered up, whereas the morphology of the negative superhump signal appears quite smooth, implying obscuration of a larger X-ray emitting region, possibly the inner accretion disc or a corona. According to our model, superhumps (both in the X-ray and optical regimes) are permitted in high-inclination LMXRBs contrary to the Haswell et al. prediction.