 One of the four cubic induced subgraphs of the unit distance graph on the three-dimensional integer lattice having a girth of 10 is isomorphic to the Laves graph.Computations suggest that the Laves graph can serve as the pattern for a metastable or perhaps unstable allotrope of carbon.Like graphite, each atom in the structure is bonded to three others, but in graphite adjacent atoms have the same bonding planes as each other whereas in this structure the bonding planes of adjacent atoms are twisted with respect to each other around the line formed by the bond, with a twisting angle of approximately 70.5°.