  Tetrahedral interactions describe the behaviour of the most abundant and
technologically important materials on Earth, such as water, silicon, carbon,
germanium, and countless others. Despite their differences, these materials
share unique common physical behaviours, such as liquid anomalies, open
crystalline structures, and extremely poor glass-forming ability at ambient
pressure. To reveal the physical origin of these anomalies and their link to
the shape of the phase diagram, we systematically study the properties of the
Stillinger-Weber potential as a function of the strength of the tetrahedral
interaction $\lambda$. We uncover a new transition to a re-entrant spinodal
line at low values of $\lambda$, accompanied with a change in the dynamical
behaviour, from Non-Arrhenius to Arrhenius. We then show that a two-state model
can provide a comprehensive understanding on how the thermodynamic and dynamic
anomalies of this important class of materials depend on the strength of the
tetrahedral interaction. Our work establishes a deep link between the shape of
phase diagram and the thermodynamic and dynamic properties through local
structural ordering in liquids, and hints at why water is so special among all
substances.
