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We propose an approach to surface reconstruction using active tactile sensing and surface normal information. Unlike previous works which consider primarily the problem of reconstructing a single tensor B-spline patch based on deformed planar or spherical domain, the surface reconstructed here is a network of triangular B-spline patches based on arbitrary topological domain and can maintain tangent plane continuity. The input is unorganized tactile sensing 3D data points with normal information of arbitrary topological type surfaces, which are obtained by a dextrous multifingered hand equipped with force/moment tactile sensors. The surface reconstructed is a parameterization of the data over these patches. An adaptive refinement is explored on the patch network in order to satisfy a given error tolerance. Demonstrations are carried out on simulated and experimental data.