The diamond or graphene lattices may be expanded theoretically by replacing one or several CC bonds of each carbon atom by the sequence C−(C≡C)k−C with k = 1, 2, etc. In this communication a systematic approach is described, by operating these replacements according to the four directions around an sp3-hybridized carbon atom (affording “mdirectional diamond-yne”) with m = 1 to 4 or the three directions around an sp2-hybridized carbon atom (affording “ndirectional graphen-yne”) with n = 1 to 3. The “n-directional graphen-yne” sheet may be folded to yield various types of directionally-expanded nanotube-ynes, nanoconeynes, nanotor-ynes, or fullrene-ynes. Analogous diynes are briefly mentioned. In addition to infinite lattices, various possibilities for molecules (diamondoid and benzenoid hydrocarbons) obtained by analogous expansions are briefly mentioned. For applications such as hydrogen storage and lithium batteries, new possibilities for selecting the shape and size of rings are available by these directional insertions of triple bonds.