Altermagnetism, a novel magnetic phase characterized by symmetry-protected, momentum-dependent spin splitting and collinear compensated magnetic moments, has thus far been explored primarily in periodic crystals. In this Letter, we extend the concept of altermagnetism to quasicrystals—aperiodic systems with long-range order and noncrystallographic rotational symmetries. Using a hyperspatial projection framework, we construct decorated Ammann-Beenker and Penrose quasicrystalline lattices with inequivalent sublattices and investigate a Hubbard model with anisotropic hopping. We demonstrate that interaction-induced Néel order on such lattices gives rise to alternating spin-polarized spectral functions that reflect the underlying quasicrystalline symmetry, revealing the emergence of unconventional $g$-wave (octagonal) and $h$-wave (decagonal) altermagnetism. Our symmetry analysis and low-energy effective theory further reveal unconventional altermagnetic spin splitting, which is compatible with quasicrystalline rotational symmetry. Our Letter shows that quasicrystals provide a fertile ground for realizing unconventional altermagnetic phases beyond crystallographic constraints, offering a platform for novel magnetisms and transport phenomena unique to quasiperiodic systems.

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• Exotic phases of matter
• Magnetic order
• Magnetism
• 2-dimensional systems
• Altermagnets
• Magnetic systems
• Quasicrystals
• Hubbard model
• Mean field theory
• Tight-binding model
• k dot p method