AbstractThe problem of constructing a smooth subdivision surface interpolating multiple intersecting curves was partially addressed in the literature. In the context of Doo-Sabin subdivision surfaces, Nasri[3] presented a solution to interpolate unlimited number of curves through an extraordinary point. In the Catmull-Clark setting, no more than two intersecting curves could so far be interpolated. That is, the interpolation of multiple intersecting curves remains a non-trivial and elusive problem. This paper puts forth a solution to this problem. The solution relies in a fundamental way on the by-now well-known notion of Catmull-Clark Polygonal Complexes introduced in [5].