We study an unusual class of carbon structures, based on rigidly interconne
cted segments of graphite. The resulting foamlike systems cover the structu
ral phase space extending from hexagonal diamond to graphite. Related to th
e most stable phases of carbon, these hybrid systems show an unusually high
structural stability at low mass densities. Our density-functional calcula
tions indicate that carbon foam is metallic, stable, and structurally rigid
.