The discoveries of fullerenes, carbon nanotubes and graphene have increased dramatically the research interests on all-carbon materials. Carbon-based materials have found applications in nanotechnology, material sciences, electronics, optic and biotechnology, occupying an important place in the development of emerging technologies. Here, we conceive a new family of carbon allotropes: Escherynes. Our predictions are based on the solid foundations of acetylenic scaffolding chemistry and first-principles calculations. In Escherynes, the carbon atoms are arranged in two types of belt-shaped rings with conjugated double and triple bonds. Our ab initio calculations reveal that (i) Escherynes are stable and viable, and can display both diamagnetic and paramagnetic ring currents in the belts, (ii) they form 'Lithium storage' complexes more stable than the similar ones formed by fullerenes, (iii) large Escherynes (>60 atoms) with Möbius structure are more stable than normal belt ones, and (iv) Möbius Escherynes display remarkable optical activity.