- Attention is directed to the conceivable possibility of finite-sized elemental benzenoids comprised solely from carbon atoms, every one of which is located only in hexagonal rings. To avoid hydrogens at boundaries, the polyhex structure then must be embedded in a finite closed surface. Mathematically there are exactly two possibilities for such surfaces: the torus and the nonorientable surface of cross-cap number 2, with the torus presumably of more chemical relevance since only it embeds into Euclidean 3-space without self-intersection. For either type of surface a systematic possibly comprehensive identification scheme is developed for consequent stereoisomeric structures, oftentimes many of which correspond to a single constitutional isomer. 1994, American Chemical Society. All rights reserved.