The Hypergraphite: A possible extension of graphitic network
  We propose a class of networks which can be regarded as an extension of the graphitic network. These networks are constructed so that surface states with non-bonding character (edge states) are formed in a tight-binding model with one orbital for each atomic site. Besides, for several networks, the tight-binding electronic structures become a zero-gap semiconductor. These properties have been found in the $\pi$-electron system of the graphene. Thus, we call these networks hypergraphite. 
Y. Takagi, M. Fujita, K. Wakabayashi, M. Igami, S. Okada, K. Nakada   and K. Kusakabe