# James Mai

My recent work has been focused upon the development of forms derived from partitions of polygon vertices. I seek to produce the complete set of forms within established parameters, and to reduce the set to the fewest number of distinct forms. "Distinct", here, means those forms that are unlike any other after reflection or rotation. A high priority in my work is to make the mathematical order of the set understandable through visual perception, apart from any verbal or mathematical description. Since there are usually multiple levels of order in a form-set, I endeavor to employ color, scale, orientation, and position to denote the various similarities and differences among the forms.

The 7 forms in “Primordial (dual partitions)” are the complete set of dual partitions of the 6 vertices of a regular hexagon. The 6 points in each form are arrayed in a circle / hexagon, and the 2 colored outlines in each form partition the 6 points in 7 distinct pairs of shapes. These 7 varieties derive from 3 simple partition types: 1 + 5 points, 2 + 4 points, and 3 + 3 points. Discounting rotations and reflections, there is one possible shape arrangement for the 1 + 5 partition (the red + green form), there are 3 possible shape arrangements for the 2 + 4 partition (the yellow + violet forms), and there are 3 possible shape arrangements for the 3 + 3 partition (the blue + orange forms).

The 17 forms in “Archaea (dual partitions)” are the complete set of dual partitions of the 8 vertices of a regular octagon. The 8 points in each form are arrayed in a circle / octagon; the colored outline and the colored shape in each form enclose the partitions. There are 4 types of dual partitions, each enclosed in its outermost ellipse or circle: 1 + 7 points yields only a single form (the central circle); 2 + 6 points yields 4 forms (bottom ellipse); 3 + 5 points yields 5 forms (upper left ellipse); and 4 + 4 points yields 7 forms (upper right ellipse). The forms are further grouped in subsets according to the number of adjacent and non-adjacent points, and colors denote the number of internal axes of reflection.