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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 thedoi:10.12941/jksiam.2012.16.1.015 fatcat:dcohz6fh7vfmfkpg4n7jkcrasm