In this paper we introduce 6-fold symmetry crystal growth using new phase-field models based on the modified Allen-Cahn equation. The proposed method is a hybrid method which uses both analytic and numerical solutions. We then show this method can be extended to $k$-fold case. The Wulff construction procedure is provided to understand and predict the shape of crystals. We also present a detailed mathematical proof of the validity of the Wulff construction. For computational results, we verify the accuracy and efficiency of the method for snow crystal growth.