When a C60 film is irradiated with a 3 kV electron-beam in an ultrahigh vacuum (base pressure: 10−7 Pa), C60 molecules are coalesced to form a one-dimensional (1D) uneven peanut-shaped C60 polymer. From a topological viewpoint, since the polymer has both positive and negative Gaussian curvatures, it can be regarded as a new allotrope of nanocarbons different from graphene, fullerenes, and nanotubes. We will present our recent results of the electronic, optical, and electron-transport properties of the 1D uneven peanut-shaped C60 polymer and discuss its novel electronic properties on the basis of quantum mechanics in Riemannian space.