For the purpose of producing more accurate confidence regions for non-symmetric continuous multivariate unimodal data we introduce and validate a method which bijectively maps the sample space by a non-linear transformation which preserves convexity of the pdf's contour-surfaces. Polygonal shaped confidence regions are defined using a generalization of the Triakis Tetrahedron to d dimensions. Comparison with distributions of higher sphericity and different decay properties become possible. A simulation study for several multi-normal non-symmetric distributions exemplifies the method's power and its criteria of applicability.