We study the dispersion of electromagnetic waves in a spatially dispersive metamaterial with Lorentz-like dependence of principal permittivity tensor components on the respective components of the wave vector performing the analysis of isofrequency contours. The considered permittivity tensor describes a triple non-connected wire medium. It is demonstrated that the metamaterial has four optic axes in the frequency range below the artificial plasma frequency. The directions of the optical axes do not depend on frequency and coincide with the diagonals of quadrants. The conical refraction effect is observed for all four optic axes.