Negatively curved graphite and triply periodic minimal surfaces

The Weierstrass representation has been used to construct negatively curved graphite in which atoms rest no a perfect triply periodic minimal surface. By applying the Bonnet transformation on a patch of the D surface decorated with graphite we have been able to construct the Gyroid and P minimal surfaces. Curvatures, densities and lattice parameters have been calculated. It has been found that the maximum Gaussian curvature for our negatively curved structures is less in magnitude than the Gaussian curvature ofC ₆₀. In addition, a new periodic graphitic set with the same topology as the I-WP minimal surface has been obtained by introducing pentagonal and octagonal rings.