The equilibrium shape of 6H-SiC nanostructures and their surfaces were studied by analyzing nano-void (similar to 10 nm) shapes, which were introduced in monocrystalline 6H-SiC by high-temperature neutron irradiation, using transmission electron microscopy. The nano-voids were determined to be irregular icosahedrons truncated with six {(1) over bar 100}, twelve {(1) over bar 103}, one smaller top-basal, and one larger bottom-basal planes, which suggests that {(1) over bar 100} and {(1) over bar 103} are the next stable surface class after the basal planes. The relatively frequent absence of the {(1) over bar 100} surface in the nano-voids indicated that the ((1) over bar 10 (3) over bar) surface type is energetically rather stable. These non-basal surfaces were found not to be atomically flat due to the creation of nanofacets with half unit-cell height in the c-axis. The {(1) over bar 100} and {(1) over bar 103} surfaces were classified as two and four face types according to their possible nanofacets and surface termination, respectively. We also discuss the surface energy difference between the ((1) over bar 10 (3) over bar) and ((1) over bar 103) face types in relation to the energy balance within the equilibrium, but irregular, polyhedron, in which the ((1) over bar 103) surface had double the surface energy of the ((1) over bar 10 (3) over bar) surface (similar to 3900 erg/cm(2)). Published by AIP Publishing.