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The design and synthesis of three-dimensional denser carbons are one of the hot issues in condensed matter physics because of their fascinating properties. Here we identify by ab initio calculations several tetragonal and monoclinic polymorphs of carbon that adopt the t32, t32*, m32, and m32* structures in P421c, P43212, P21/c, and C2 symmetry, respectively. These carbon polymorphs have large 32-atom unit cells in all-sp3 bonding networks comprising five- and six-membered rings that are dynamically stable, as verified by a phonon mode analysis. Electronic band structure calculations show that they are insulators with band gaps in the range of 5.19-5.41 eV, close to the calculated band gap of 5.34 eV for diamond. Remarkably, these carbon phases possess an extremely high atom number density exceeding that of diamond. The present results establish different types of carbon phases and offer insights into their outstanding structural and electronic properties. [ABSTRACT FROM AUTHOR]