Mesh adaptation is key for accurate numerical simulation of complex multiscale phenomena. While well-established for simplicial, Cartesian, and hexahedral discretizations, mesh adaptation for general polytopal meshes remains an active research area. This work presents a new polytopal adaptation strategy implemented in the Parallel Dual Meshing Tool (PDMT), utilizing dual-mesh construction driven by a seed set connected via an auxiliary triangulation. The generated polytopal mesh P constructed using the seeds is the smooth dual partition of the auxiliary triangulation with boundary clipping. For this work, given a Discontinuous Galerkin (DG) numerical solution u_h, a Riemannian metric tensor field M(u_h) to drive the polytopal adaptation is employed. To minimize L^p interpolation error, the optimal M is derived from the reconstructed Hessian H. The adaptation process aims to generate a unit mesh in the resulting Riemannian metric space. This requires that all edges of the auxiliary triangulation satisfy the unit length condition in the metric space. This allows mapping robust simplicial Hessian-based isotropic and anisotropic adaptation strategies directly to polytopal meshes. The adapted edges govern the interaction between seeds, resulting in an adapted mesh. A non-trivial demonstration of isotropic/anisotropic polytopal mesh adaptation via the presented method is illustrated through DG simulations, showing strong alignment with features like boundary layers and shocks.