  The detection of two similar periodicities (3001 and 3028 s) in the light
curve of V1405 Aql, 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 Aql 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 Aql 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 Aql as a permanent superhump
system. The 14-year 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. According to our model superhumps (both in
the X-ray and optical regimes) are permitted in high inclination LMXRBs
contrary to Haswell et al. (2001) prediction.
