  We explore the phase structure of dense magnetized quark matter when a
repulsive vector interaction, parametrized by $G_V$, is present. Our results
show that for a given magnetic field intensity ($B$) one may find a value of
$G_V$ for which quark matter may coexist at three different baryonic density
values leading to the appearance of two triple points in the phase diagram
which have not been observed before. Another novel result is that at high
pressure and low temperature we observe a first order transition which presents
a negative slope in the $P-T$ that is reminiscent of the solid-liquid
transition line observed within the water phase diagram. These unusual patterns
occur for $G_V$ and $B$ values which lie within the range presently considered
in many investigations related to the study of magnetars.
