In this paper, the propagation of acoustic waves in the phononic crystals (PC) of 3D with rhombohedral(II) lattice is studied theoretically. The PC are constituted of nickel spheres embedded in epoxy. The calculations of the band structure and density of states are performed with the plane wave expansion method in the irreducible part of the Brillouin zone (BZ). In this study, we analyze the dependence of the band structures inside (the complete band gap width) and outside the complete band gap (negative refraction of acoustic wave) on the lattice angle in the irreducible part of the first BZ. Also the effect of lattice angle has been analyzed on the band structure of the ( $$ \bar{1}10 $$ 1 ¯ 10 ) and (122) planes. Then, the equifrequency surface is calculated for the high symmetry point in the [111] and [100] directions. The results show that the maximum width of AEBG (0.022) in the irreducible part of the BZ of RHL2 is formed for (105∘) and no AEBG is found for γ > 150∘. Also, the maximum of the first and second AEBG width are 0.1076 and 0.0523 for γ = 133∘ in the ( $$ \bar{1}10 $$ 1 ¯ 10 ) plane and the maximum of the first and second AEBG width are 0.1446 and 0.0998 for γ = 113∘ in the (122) plane. In addition, we have found that frequencies in which negative refraction occurs is constant for all lattice angles.