A novel stable crystal structure is discovered in a variety of $AB{O}_{3},AB{F}_{3}$, and ${A}_{2}{O}_{3}$ compounds, via the use of first principles. This novel structure appears under hydrostatic pressure, and can be considered to be a post-post-perovskite phase. It provides a successful solution to experimental puzzles in important systems and is characterized by one-dimensional channels linked by a group of two via edge-sharing oxygen/fluorine octahedra. Such organization automatically results in anisotropic elastic properties and new magnetic arrangements. Depending on the system of choice, this post-post-perovskite structure also possesses electronic band gaps ranging from zero to $\ensuremath{\simeq}10\mathrm{eV}$ being direct or indirect in nature.