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Three-dimensional (3D) metamorphosis is a powerful technique to produce a 3D shape transformation between two or more existing models. We propose a novel 3D morphing technique that avoids creating a merged embedding that contains the faces, edges, and vertices of two given embeddings. This novel 3D morphing technique dynamically adds or removes vertices to gradually transform the connectivity of 3D polyhedrons from a source model into a target model and simultaneously creates the intermediate shapes. In addition, a priority control function provides the animators with control of arising or dissolving of input models' features in a morphing sequence. This is a useful tool to control a morphing sequence more easily and flexibly. Several examples of aesthetically pleasing morphs are demonstrated using the proposed method.