# James Mai

My recent work has been focused upon the development of sets of geometric forms generated from permutational and combinatorial methods. The forms in each set are at once similar, in that all forms share the same geometric features, and different, in that each form is a unique arrangement of those features. As important, each form-set is both complete, in that all permutations/combinations are present, and non-redundant, in that no two forms are the same, even after rotation or reflection. I employ color, position, scale, and grouping to show the similar and different features among the forms so that the mathematical order may be understood by vision, apart from any verbal or mathematical description.

The 7 forms in “Primordial (hexagons)” are the complete set of 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 12 forms in “Familial (octagons)” are the complete set of circuits joining the 8 vertices of an octagon, where 4 outer edges of the octagon are preserved and the form possesses either reflective or rotational symmetry. The large white circles indicate symmetry characteristics; from top to bottom: 2 forms are rotational, 5 forms possess 1 axis of reflection, 3 forms possess 2 axes, and 1 form possesses 4 axes. Additionally, this form-set shows 5 distinct arrangements of the 4 outer edges (black lines). These 5 groups are distinguished by colors (blue, orange, yellow, red, green). This group of 12 symmetrical forms is a subset of a larger superset of 202 octagon circuit-forms.