  A three-dimensional elemental carbon Kagome lattice (CKL), made of only
fourfold coordinated carbon atoms, is proposed based on first-principles
calculations. Despite the existence of 60{\deg} bond angles in the triangle
rings, widely perceived to be energetically unfavorable, the CKL is found to
display exceptional stability comparable to that of C60. The system allows us
to study the effects of triangular frustration on the electronic properties of
realistic solids, and it demonstrates a metal-insulator transition from that of
graphene to a direct gap semiconductor in the visible blue region. By
minimizing s-p orbital hybridization, which is an intrinsic property of carbon,
not only the band edge states become nearly purely frustrated p states, but
also the band structure is qualitatively different from any known bulk
elemental semiconductors. For example, the optical properties are similar to
those of direct-gap semiconductors GaN and ZnO, whereas the effective masses
are comparable or smaller than those of Si.
