Abstract: This paper presents a simple algorithm for associating a smooth, low-degree polynomial surface with triangulations whose extraordinary mesh nodes are separated by sufficiently many ordinary, 6-valent mesh nodes. Output surfaces are at least tangent continuous and are C² sufficiently far away from extraordinary mesh nodes; they consist of three-sided Bé;zier patches of degree 4. In particular, the algorithm can be used to skin a mesh generated by a few steps of Loop's generalization of three-direction box-spline subdivision.