A ternary six-point interpolating subdivision scheme for a closed polygon is constructed first. Then it is extended to an open polygon. The scheme is analyzed by using the Laurent polynomial method. It is shown that the scheme is

${C}^{2}$ continuous over a certain fairly small parametric open interval. It is shown that the scheme has approximation order 4. Finally, using the techniques in [

*C. Beccari*,

*G. Casciola* and

*L. Romani*, Comput. Aided Geom. Des. 24, No. 4, 210–219 (2007;

Zbl 1171.65326)] it is shown that the support of the scheme is smaller than the support of the corresponding scheme in [

*A. Weissman*, A six-point interpolation scheme for curve design. M.Sc. Thesis. Tel Aviv University (1990)].