Toranosuke Matsubara,1 Akihisa Koga,1 Atsushi Takano,2 Yushu Matsushita,3 and Tomonari Dotera41-Department of Physics, Tokyo Institute of Technology, Meguro, Tokyo 152-8551, Japan2-Department of Molecular and Macromolecular Chemistry,Nagoya University, Nagoya, Aichi 464-8603, Japan3-Toyota Physical and Chemical Research Institute, Nagakute, Aichi 480-1192, Japan4-Department of Physics, Kindai University, Higashi-Osaka, Osaka 577-8502, JapanAperiodic crystals constitute a fascinating class of materials that includes incommensurate (IC) modulated structures [1, 2] and quasicrystals (QCs) [3–8]. Although these two categories share a common foundation in the concept of superspace, the relationship between them has remained enigmatic and largely unexplored. Here, we show “any metallic-mean” QCs [9–11], surpassing the confines of Penrose-like structures, and explore their connection with IC modulated structures. In contrast to periodic approximants of QCs [12, 13], our work introduces the pivotal role of “aperiodic approximants” [14], articulated through a series of k-th metallic-mean tilings serving as aperiodic approximants for the honeycomb crystal, while simultaneously redefining this tiling as a metallicmean IC modulated structure, highlighting the intricate interplay between these crystallographic phenomena. We extend our findings to real-world applications, discovering these unique tiles in a terpolymer/homopolymer blend [15] and applying our QC theory to a colloidal simulation displaying planar IC structures [16, 17]. In these structures, domain walls are viewed as essential components of a quasicrystal, introducing additional dimensions in superspace. Our research provides a fresh perspective on the intricate world of aperiodic crystals, shedding light on their broader implications for domain wall structures across various fields [18, 19].