  We considered a two dimensional three electron quantum dot in a magnetic
field in the Wigner limit. A unitary coordinate transformation decouples the
Hamiltonian (with Coulomb interaction between the electrons included) into a
sum of three independent pair Hamiltonians. The eigen-solutions of the pair
Hamiltonian provide a spectrum of pair states. Each pair state defines the
distance of the two electrons involved in this state. In the ground state for
given pair angular momentum $m$, this distance increases with increasing $|m|$.
The pair states have to be occupied under consideration of the Pauli exclusion
principle, which differs from that for one-electron states and depends on the
total spin $S$ and the total orbital angular momentum $M_L=\sum m_i$ (sum over
all pair angular momenta). We have shown that the three electrons in the ground
state of the Wigner molecule form an equilateral triangle (as might be
expected) only, if the state is a quartet ($S=3/2$) and the orbital angular
momentum is a magic quantum number ($M_L=3 m ; m=$ integer). Otherwise the
triangle in the ground state is isosceles. For $M_L=3 m+1$ one of the sides is
longer and for $M_L=3 m-1$ one of the sides is shorter than the other two.
