Compactifications of moduli of elliptic K3 surfaces: Stable pair and toroidal

We describe two geometrically meaningful compactifications of the moduli space elliptic K3 surfaces via stable slc pairs, for different choices a polarizing divisor, and show that their normalizations are toroidal space, one ramification divisor another rational curve divisor. In course proof, we further develop theory integral affine spheres with 24 singularities. also construct (generalized) types ${\bf A_n}$ ($n\ge1$), C_n}$ ($n\ge0$) E_n}$ ($n\ge0$).