  We found a class of triangulated surfaces in Euclidean space which have
similar properties as isothermic surfaces in Differential Geometry. We call a
surface isothermic if it admits an infinitesimal isometric deformation
preserving the mean curvature integrand locally. We show that this class is
M\"{o}bius invariant. Isothermic triangulated surfaces can be characterized
either in terms of circle patterns or based on conformal equivalence of
triangle meshes. This definition generalizes isothermic quadrilateral meshes.
  A consequence is a discrete analog of minimal surfaces. Here the Weierstrass
data needed to construct a discrete minimal surface consist of a triangulated
plane domain and a discrete harmonic function.
