The local geometry, electronic structure, and vibrational features of three vicinal double interstitial defects in diamond, ICIC, ICIN, and ININ, are investigated and compared with those of three "simple" ⟨100⟩ interstitial defects, ICC, ICN, and INN, previously reported by Salustro et al. [Phys. Chem. Chem. Phys. 20, 16615 (2018)], using a similar quantum mechanical approach based on the B3LYP functional constructed from Gaussian-type basis sets, within a supercell scheme, as implemented in the CRYSTAL code. For the first time, the Fermi contact term and hyperfine coupling tensor B of the four open shell structures, ICIC, ICIN, ICC, and ICN, are evaluated and compared with the available experimental EPR data. For the two double interstitial defects, the agreement with experiment is good, whereas that for the single interstitials is found to be very poor, for which a likely reason is the incorrect attribution of the EPR spectra to uncertain atomic details of the microstructure of the samples. The infrared spectra of the three double interstitial defects exhibit at least two peaks that can be used for their characterization.