Graphite may be viewed as a low-surface-energy carbon allotrope with little layer-layer interaction. Other low-surface-energy allotropes but with much stronger layer-layer interaction may also exist. Here, we report a first-principles prediction for one of the known carbon allotropes, bcc-C6 (a body centered carbon allotrope with six atoms per primitive unit), that should have exceptionally low-surface energy and little size dependence down to only a couple layer thickness. This unique property may explain the existence of the relatively-high-energy bcc-C6 during growth. The electronic properties of the bcc-C6 thin layers can also be intriguing: the (111), (110), and (001) thin layers have direct band gap, indirect band gap, and metallic character, respectively. The refrained chemical reactivity of the thin layers does not disappear after cleaving, as lithium-doped (Li-doped) 3-layers (111) has a noticeably increased binding energy of H2 molecules with a maximum storage capacity of 10.8 wt %.