The influence of a crystallographic symmetry break on the morphology of precipitates during the coherent precipitation of a trigonal phase in a close packed hexagonal matrix is analyzed. It is pointed out that in spite of the isotropy of the stress free strain of the precipitate in the basal plane, the existence of an extra elastic constant in the precipitate (associated to the loss of symmetry) induces a morphological evolution from a shape having a symmetry of revolution around the threefold axis to a needle-like one oriented along the compact directions in the basal plane. These general considerations are applied to the case of zêta zirconium hydrides the crystallography of which has been recently identified to be coherent with that of the alpha Zr matrix. The influence of symmetry break and elastic heterogeneity on precipitation morphology has been numerically addressed by using different approaches. An analytical approximation to the elastic energy based on Eshelby equivalent inclusion method allows obtaining a qualitative criterion to determine the occurrence of a shape bifurcation of zêta hydrides.