Modelling of processes involving deep Earth liquids requires information on their structures and compression mechanisms. However, knowledge of the local structures of silicates and silica (SiO2) melts at deep mantle conditions and of their densification mechanisms is still limited. Here we report the synthesis and characterization of metastable high-pressure silica phases, coesite-IV and coesite-V, using in situ single-crystal X-ray diffraction and ab initio simulations. Their crystal structures are drastically different from any previously considered models, but explain well features of pair-distribution functions of highly densified silica glass and molten basalt at high pressure. Built of four, five-, and six-coordinated silicon, coesite-IV and coesite-V contain SiO6 octahedra, which, at odds with 3rd Pauling's rule, are connected through common faces. Our results suggest that possible silicate liquids in Earth's lower mantle may have complex structures making them more compressible than previously supposed.