MgSiO3 perovskite is the most abundant mineral in the Earth’s lower mantle. A structural phase transition in this phase to a CaIrO3-type polymorph was discovered in 2004 (Murakami et al. 2004; Oganov and Ono 2004; Tsuchiya et al. 2004). This new polymorph, the so-called post-perovskite (PPV) phase, was produced at pressures and temperatures close to those expected at the core-mantle boundary, 125 GPa and 2,500 K (Murakami et al. 2004). In the Earth, the PPV phase is the final form of MgSiO3. This surprising discovery invited a new question: what is the next polymorph of MgSiO3? MgSiO3 PPV consists of SiO3 layers intercalated by magnesium (Fig. 1⇓). Therefore, it is natural to expect still other pressure induced transitions to more isotropic close-packed looking structures. This question has acquired further importance since the discovery of terrestrial-type exoplanets: the Super-Earth planet with ~7 Earth masses, GJ876d (Rivera et al. 2005), and the Saturn-like planet with a massive dense core with ~67 Earth masses, D149026b (a dense-Saturn) (Sato et al. 2005). Many others have been found since then. Pressures and temperatures in the mantle of these planets are much higher than in the Earth. There is also a pressing need to understand and model matter in the core of the giants, particularly the solar ones, Jupiter, Saturn, Uranus, and Neptune. In GJ876d, pressure and temperature at its core-mantle boundary was roughly estimated to be ~1 TPa (10 Mbar) and ~4,000 K (Valencia et al. 2006). The gas giants, Jupiter and Saturn, and the icy giants, Uranus and Neptune, have small dense cores surrounded by hydrogen/helium and ice, respectively. Pressures and temperatures at the core-envelope boundaries of these planets have been estimated to be 40 Mbar and 15,000~20,000 K in Jupiter, 10 …