  We introduce a general mechanism for obtaining Weyl points in a stack of 2D
quasicrystals, which can be extended to any stack of aperiodic layers. We do so
by driving a topological phase transition with the vertical crystal-momentum as
the tuning parameter, which leads to gap closures at the critical points
sourcing Berry curvature. To illustrate, we use a simple 3D generalization of
the Qi-Wu-Zhang model defined on a Penrose quasicrystal. The presence of Weyl
points is established via the local Chern marker, projected band structure and
density of states. Interestingly, we uncover an analogue of Fermi arcs in the
quasicrystalline setting, which we deem Fermi-Bragg arcs, densely distributed
lines connecting the band degeneracies and indexed by the Bragg peaks.
Signatures of such surface states in quantum oscillations and the prospect of a
fully quasicrystalline Weyl system are also discussed. The flexibility of our
proposal brings new opportunities for realizing other gapless topological
phases in aperiodic systems, paving the way for a significantly expanded role
for topological band theory.
