Bilayer graphene exhibits outstanding characteristics that can be modified by adjusting the twist angle between two layers. An exact ${30}^{\circ }$-twisted bilayer graphene forms a material comprising two-dimensional quasicrystals accompanied by a relativistic Dirac fermion. In this study, the atomic arrangements of quasicrystal bilayer graphene on a SiC(0001) substrate are identified using positron diffraction. The interlayer distance in quasicrystal bilayer graphene is determined to be 3.46 Å, revealing an expansion of 0.17 Å as compared with that of Bernal-stacked bilayer graphene. This result provides important insights for elucidating the origin of the magnitude of coupling between graphene layers.

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• Cellular bilayers
• Quasicrystalline structure
• Graphene
• van der Waals systems
• Reflection high-energy electron diffraction