  Recently, it is discovered that a certain class of nanocarbon materials has
geometrical properties related to the discrete geometry, pre-constant discrete
principal curvature [9] based on the discrete surface theory proposed on
trivalent graphs by Kotani, Naito and Omori [10]. In this paper, with the aim
of an application to the nanocarbon materials, we will study discrete constant
principal curvature (CPC) surfaces. Firstly, we developed the discrete surface
theory on a full 3-ary oriented tree so that we define a discrete analogue of
principal directions on them to investigate it. We also construct some
interesting examples of discrete constant principal curvature surfaces,
including discrete CPC tori.
