  The emergence of two-band nodal points (i.e. Weyl nodes) in gapless
topological phases only requires translational symmetry, however, their
necessary existence in the electronic band structure of materials can be
deduced when additional crystalline symmetries are present. In particular,
rotation symmetries have been known to be able to protect Weyl nodes of high
chirality. In this work, we identify ReO$_3$ as an ideal high-chirality Weyl
semimetal in which hexagonal screw symmetry plays a crucial role. To show this,
we revisit in detail the algebraic determination of the chirality of Weyl nodes
from the spinful irreducible representations of occupied bands, and combine it
with the complementary $C_{2}T$-symmetry-protected patch Euler class that
indicates the pinning of the Weyl nodes on $C_{2}T$-invariant planes.
Supporting our findings with first-principles calculations, we furthermore
reveal very clear Fermi arc signatures of the high-chirality Weyl nodes at the
Fermi level and for different surface orientations. We finally consider the
effect of strain upon which the reconfiguration of Weyl nodes further unveils
their Chern (i.e. high chirality) and Euler (i.e. symmetry-plane pinning)
topological nature.
