1. An apparatus for compressing a three-dimensional (3D) mesh, the apparatus comprising: a mesh simplifying unit to generate a base mesh by simplifying an inputted 3D mesh, thereby eliminating at least one vertex; a base mesh coding unit to code the base mesh; a vertex coding unit to code, based on a covariance matrix, the at least one vertex eliminated by the simplification; and an entropy coding unit to entropy-code the coded base mesh and the coded at least one vertex into a bit stream by performing entropy-coding.