Quasicrystals are not spatially periodic, yet they exhibit long-range order. These aperiodic crystals feature rotational symmetries that are mathematically forbidden in periodic crystals. In 1984, Shechtman performed X-ray diffraction measurements on a metallic alloy, revealing 10-fold rotational symmetry in the diffraction pattern, which was thought to be impossible. This work eventually led to the redefinition of what constitutes a crystal, and the recognition of the reality of aperiodic crystals. Shechtman was then awarded the 2011 Nobel prize in chemistry for the discovery of aperiodic crystals. In recent decades, band structure and its interplay with topology have provided deep insight into intriguing behavior in periodic crystalline quantum materials. However, thirty years after the discovery of aperiodic crystals, the role of the energy spectrum and its interplay with topology is not well-understood for quasicrystals because standard theoretical methods used to study the energy spectrum of a crystal has relied on translational symmetry. An experimental apparatus that can emulate the quantum physics of quasicrystals would open a window into quasicrystalline “band structure” and topology that is difficult to access with theoretical and analytical methods alone. This talk will describe the design of such an apparatus, in which a quantum gas is confined within a 10-fold rotation-symmetric quasiperiodic optical lattice and will mention planned first measurements.