Since the advent of transformation optics and scattering cancelling technology, a plethora of unprecedented metamaterials, especially invisibility cloaks, have been successfully demonstrated in various communities, e.g., optics, acoustics, elastic mechanics, dc electric field, dc magnetic field, and thermotics. A long-held captivation is that transformation-optic metamaterials of anisotropic or noncentrosymmetric geometry (e.g., ellipsoids) commonly come along with parameter approximation/simplification or directional functions. Here, a synthetic paradigm with strictly full parameters and omnidirectionality is reported simultaneously to address this long-held issue for molding heat flow and experimentally demonstrate a series of noncentrosymmetric thermal metadevices. It changes the usual perception that transformation thermotic/dc/acoustic metamaterials are just a direct and simplified derivatives of the transformation-optic counterpart. Instead, the proposed methodology solves an intriguingly important and challenging problem that is not possibly achievable for transformation-optic metamaterials. The approach is rigorous, exact, robust, and yet elegantly facile, which may open a new avenue to manipulating the Laplacian and wave-dynamic fields in ways previously inconceivable.