This protocol introduces a method for generating strictly controlled and objectively defined stimuli for figure recognition experiments. A (6, n) figure consists of n line segments that are spanned between n pairs of points located at the vertices of an invisible regular hexagon. The structural properties (graph invariants) and superficial features (non-graph invariants) of each (6, n) figure with n values ranging from 1 to 6 are calculated and stored in a database. Using this database, experimenters can systematically extract appropriate figures depending on the purpose of the experiment. Furthermore, if the database does not contain necessary information, new feature values can sometimes be calculated ad hoc from the formation of a specific (6, n) figure. Let us call a mirror-reflected pair of figures an axisymmetric (Ax) pair. An Ax pair of figures is known to be more difficult to discriminate than a non-identical pair in the decision of whether the shapes of a given pair are rotated-to-be-identical (Idr). The purpose of the present experiment is to examine whether the sameness of line lengths between two figures in a pair causes the discrimination of the pair to be as difficult as that of an Ax pair. Mutually isomorphic figures share common structural properties despite differences in shape. Ax pairs and Idr pairs are special cases of isomorphic pairs. Furthermore, an Ax pair and Idr pair share most of the superficial feature values, except the relative direction from one location to another location across an axis of symmetry is opposite for an Ax pair. Three types of mutually isomorphic (6, 4) figure pairs were generated: Idr; Ax; and non-identical, non-axisymmetric, isomorphic (Nd) pairs. Nd pairs were further classified into three subcategories according to the superficial feature values of the degree of line length differences.