Dihedral-Angle Sums in Orthocentric, Power-k, and Isodynamic Tetrahedra

Abstract

Let Σ(T) be the sum of the six internal dihedral angles of a nondegenerate Euclidean tetrahedron. This paper organizes several special families around the Power-k relation d_ij^k = y_i + y_j. It proves the sharp orthocentric lower bound and exact range, the positive Power-2 range, the universal ranges for k<1 and k>2, and the complete isodynamic case.

The interval 1<k<2 remains an explicitly labelled conjectural regime. The paper proves a strict local minimum at the regular tetrahedron and gives feasibility and numerical evidence while separating those claims from the rigorous theorems.