  The structure of the lowest states of a three-electron axially symmetric
parabolic quantum dot in a zero magnetic field is investigated. It is shown
that the electronic density of the triplet states possesses certain approximate
symmetry which is best seen when using Dalitz plots as the visualization tool.
It is demonstrated that the origin of that symmetry is caused by the symmetry
of the potential energy in the vicinity of its minimum. The discovered symmetry
could provide an insight into the problem of the separation of slow and fast
variables in the Schro\"dinger equation for the axially or spherically
symmetric quantum dots.
