  Characterizing a microlensing planet is done from modeling an observed
lensing light curve. In this process, it is often confronted that solutions of
different lensing parameters result in similar light curves, causing
difficulties in uniquely interpreting the lens system, and thus understanding
the causes of different types of degeneracy is important. In this work, we show
that incomplete coverage of a planetary perturbation can result in degenerate
solutions even for events where the planetary signal is detected with a high
level of statistical significance. We demonstrate the degeneracy for an
actually observed event OGLE-2012-BLG-0455/MOA-2012-BLG-206. The peak of this
high-magnification event $(A_{\rm max}\sim400)$ exhibits very strong deviation
from a point-lens model with $\Delta\chi^{2}\gtrsim4000$ for data sets with a
total number of measurement 6963. From detailed modeling of the light curve, we
find that the deviation can be explained by four distinct solutions, i.e., two
very different sets of solutions, each with a two-fold degeneracy. While the
two-fold (so-called "close/wide") degeneracy is well-understood, the degeneracy
between the radically different solutions is not previously known. The model
light curves of this degeneracy differ substantially in the parts that were not
covered by observation, indicating that the degeneracy is caused by the
incomplete coverage of the perturbation. It is expected that the frequency of
the degeneracy introduced in this work will be greatly reduced with the
improvement of the current lensing survey and follow-up experiments and the
advent of new surveys.
