This study investigated the determinants of the canonical view to recognize the three-dimensional structure of an object with self-occluded parts using a quantitative analysis of line drawings of novel polyhedral objects in terms of the geometrical properties. The results showed that 65% of drawings properly illustrated the whole structure and configuration of polyhedra. Although different accidental and generic views could be obtained for each polyhedra, the drawings showed a strikingly similar view. In more than 80% of proper drawings subjects chose a generic view by which the constituent surfaces could be observed maximally. The results suggested that the canonical view of a polyhedron (1) included the maximum number of observable surfaces, (2) exposed the features of configuration, and (3) was one of the generic views, which had a stable topological structure in spite of the variance of viewpoint in the wider range.