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Analyses of metallic amorphous solids constructed using molecular dynamics (MD) simulations have demonstrated that individual short-range orders (SROs) are linked with neighboring SROs and form various medium-range orders (MROs). These MROs have been observed to have different structural stability depending on their linking patterns. On the basis of the assessment of the structural stability of various MROs, we propose new types of structural organization, namely, icosahedral medium-range orders (I-MROs) and their extended-range order that forms the backbone of amorphous solids. We also discuss why the atomic-scale structure of an amorphous alloy can be more appropriately described in terms of I-MROs, rather than by the degree of short-range ordering as characterized by the fractions of SROs.