In continuation of \cite{HHOT}, we discuss the question of spectral minimal
3-partitions for the rectangle ]−2a,2a[×]−2b,2b[, with 0<a≤b. It has been observed in \cite{HHOT} that when
0<ba<83 the minimal 3-partition is obtained by the three
nodal domains of the third eigenfunction corresponding to the three rectangles
]−2a,2a[×]−2b,−6b[, ]−2a,2a[×]−6b,6b[ and ]−2a,2a[×]6b,2b[. We will describe a possible mechanism of transition for increasing
ba between these nodal minimal 3-partitions and non nodal minimal
3-partitions at the value 83 and discuss the existence of
symmetric candidates for giving minimal 3-partitions when 83<ba≤1. Numerical analysis leads very naturally to nice questions
of isospectrality which are solved by introducing Aharonov-Bohm Hamiltonians or
by going on the double covering of the punctured rectangle