The notion that a regular icosahedron is unattainable in neutral B12H12 has persisted for nearly 70 years. This is because 24 valence electrons are used for B-H bonds, while another 24 electrons are necessary to maintain the deltahedron, unlike the 26 used in the dianion. According to Wade-Mingos rules, the neutral system should be a deltahedron with a capped face. Nevertheless, our exploration of the potential energy surface of B12H12 reveals that the global minimum is a closed-shell form with an H2 unit attached to a boron vertex of B12H10, preserving the deltahedral boron skeleton.