  The interlayer coupling can be used to engineer the electronic structure of
van der Waals heterostructures (superlattices) to obtain properties that are
not possible in a single material. So far research in heterostructures has been
focused on commensurate superlattices with a long-ranged Moir\'e period.
Incommensurate heterostructures with rotational symmetry but not translational
symmetry (in analogy to quasicrystals) are not only rare in nature, but also
the interlayer interaction has often been assumed to be negligible due to the
lack of phase coherence. Here we report the successful growth of
quasicrystalline 30{\deg} twisted bilayer graphene (30{\deg}-tBLG) which is
stabilized by the Pt(111) substrate, and reveal its electronic structure. The
30{\deg}-tBLG is confirmed by low energy electron diffraction and the
intervalley double-resonance Raman mode at 1383 cm$^{-1}$. Moreover, the
emergence of mirrored Dirac cones inside the Brillouin zone of each graphene
layer and a gap opening at the zone boundary suggest that these two graphene
layers are coupled via a generalized Umklapp scattering mechanism, i.e.
scattering of Dirac cone in one graphene layer by the reciprocal lattice vector
of the other graphene layer. Our work highlights the important role of
interlayer coupling in incommensurate quasicrystalline superlattices, thereby
extending band structure engineering to incommensurate superstructures.
