A data structure for representing a general n-dimensional polygonal mesh. The data structure includes a structure record and a data record for each three dimensional shape. The structural record contains polygonal model connectivity information and further includes a stitching record that defines corresponding polygonal (triangular) mesh edge pairs and a polygonal (triangular) tree record representing a polygon (triangle) tree. The stitching record includes a vertex tree and a set of jump edges. The data record includes at least three polygonal records, each corresponding to a polygon. Each polygonal record is associated with a face of said polygonal model and classifies its corresponding polygon as either a leaf polygon, a running polygon or a branching polygon. Polygonal shapes are encoded into the data structure by first building a spanning tree for the polygonal mesh. A set of cut edges are derived for the polygonal mesh. The stitching record is constructed for the set of cut edges. Then traversing the polygon tree, the data records are encoded. The encoded data is transmitted, the structure record being transmitted first, followed by the data record. The stitching tree and polygon tree are decoded as they are received and, after at least three polygons are received, received polygons may be displayed.