We discover an eg-orbital (dz2,dx2-y2) model within the diamond lattice (eg-diamond model) that hosts novel topological states. Specifically, the eg-diamond model yields a three-dimensional (3D) nodal cage (3D-NC), which is characterized by a d-d band inversion protected by two types of degenerate states (i.e., eg-orbital and diamond-sublattice degeneracies). We demonstrate materials realization of this model in the well-known spinel compounds (AB2X4), where the tetrahedron-site cations (A) form the diamond sublattice. An ideal half metal with one metallic spin channel formed by well-isolated and half-filled eg-diamond bands, accompanied by a large spin gap (4.36 eV) is discovered in one 4-2 spinel compound (VMg2O4), which becomes a magnetic Weyl semimetal when spin-orbit coupling effect is further considered. Our discovery greatly enriches the physics of diamond structure and spinel compounds, opening a door to their application in spintronics.