The band structures include 3N bands: three acoustic modes starting from zero energy (ω = 0) at the  point (the center of the Brillouin zone) up to a few terahertz, and 3N-3 optical modes at higher energies. The acoustic modes correspond to the rigid translation modes of the crystal (two transverse and one longitudinal). All panels in Fig. show positive phonon frequencies, indicating the dynamic stability of all three new carbon allotropes.