A systematic computational study on the crystal structure of n-diamond has been performed using first-principle methods. A novel carbon allotrope with hexagonal symmetry R32 space group has
been predicted. We name it as HR-carbon. HR-carbon composed of lonsdaleite layers and unique C3 isosceles triangle rings, is stable over graphite phase above 14.2 GPa. The simulated x-ray diffraction pattern, Raman, and energy-loss near-edge spectrum can match the experimental results very well, indicating that HR-carbon is a likely candidate structure for n-diamond. HR-carbon has an incompressible atomic arrangement because of unique C3 isosceles triangle rings. The hardness and bulk modulus of HR-carbon are calculated to be 80 GPa and 427 GPa, respectively, which are comparable to those of diamond. C3 isosceles triangle rings are very important for the stability and hardness of HR-carbon.