  Given the best-fit results of six neutrino oscillation parameters, we plot
the Dirac and Majorana unitarity triangles (UTs) of the 3\times 3 lepton flavor
mixing matrix to show their real shapes for the first time. The connections of
the Majorana UTs with neutrino-antineutrino oscillations and neutrino decays
are explored, and the possibilities of right or isosceles UTs are discussed. In
the neutrino mass limit of m_1 \to 0 or m_3 \to 0, which is allowed by current
experimental data, we show how the six triangles formed by the effective
Majorana neutrino masses \langle m\rangle_{\alpha\beta} (for \alpha, \beta = e,
\mu, \tau) and their corresponding component vectors look like in the complex
plane. The relations of such triangles to the Majorana phases and to the
lepton-number-violating decays H^{++} \to \alpha^+ \beta^+ in the type-II
seesaw mechanism are also illustrated.
