A new carbon family adopting wavy structures has been found by quantum chemical calculations. The key motif of this family is a condensed four-membered ring. Periodically wavy-carbon sheets (wavy-C, sheets, n = 2, 6, and 8) as well as wavy-C-36 tube were found to be very similar to the previously reported prism-C-n carbon tubes (n = 5, 6, and 8) in several respects, including the relative energies per one carbon atom with respect to graphene, CC bond lengths, and CCC bond angles. Because of very high relative energies with respect to graphene (206-253 kJ mol(-1)), the wavy-carbons may behave as energy reserving materials. (C) 2015 Elsevier B.V. All rights reserved.