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Nonphononic vibrations originating from disordered structures have garnered significant attention as a fundamental feature of glasses that distinguishes them from crystals. Recently, we discovered that one-dimensional (1D) stringlike vibrations without volume change are responsible for the boson peak in the reduced density of states of two-dimensional (2D) glasses [Y.-C. Hu and H. Tanaka, Nat. Phys. 18, 669 (2022)1745-247310.1038/s41567-022-01628-6]. Here we investigate the vibrational properties of three-dimensional (3D) model glasses with isotropic repulsive and attractive interactions and find that the boson peak arises from stringlike quasilocalized transverse vibrations in these 3D systems. These results suggest that stringlike vibrations are the universal origin of the boson peak in both 2D and 3D model glasses, as long as the interaction is isotropic. Furthermore, we confirm that the characteristic frequency of the quasilocalized transverse vibrations, i.e., the boson peak frequency, coincides with the Ioffe-Regel limit of transverse phonons. These results imply the boson peak originates from the frequency-resonant scattering of transverse phonons by quasilocalized vibrations rather than phonon scattering due to elastic inhomogeneity. Our findings provide insights into the origin of low-temperature glass anomalies and inspire further research.