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JIAN Xin-hua,

Each of 12 like squares, with one of its diagonal axes tangent to a circle, link vertex to vertex around the circle. The other diagonals of the 12 squares fall on six axes (in transverse pairs, two to one axis) that intersect at the circle's center. The squares' outer set of the 12 vertices and their inner set of 12 vertices describe two concentric, regular dodecagons. Aside from the 12 squares, the band between thetwo dodecagons is compartmented into 12 equilateral triangles and 12 isosceles triangles. Similar concentric bands of this same makeup, replicated both inwardly and outwardly, configure into the disk of a compound geometric spiral.

In each dodecagonal band, three sets of four squares gestalt into three larger squares; and four sets of three equilateral triangles gestalt into four larger equilateral triangles. Mechanically drawing the lacking lines (which are wont to be provided by the perceiving eye) between the edges of the smaller square to complete the larger squares and between the smaller equilateral triangles to complete the larger equilateral triangles produces a network that accommodates a two-color map treatment. Four colors, however, can facilitate the definition of and distinction between squares and triangles: Green and blue bring out alternating squares; red and orange bring out alternating triangles.

Since numerous squares and equilateral triangles are embedded in the reticulation of this compound spiral, only one of the three emergent squares and only one of the four emergent triangles are, through coloration, elaborated at each level. Starting with the figuration of the outermost square, the square at the next level is rotated clockwise, by one interval, into its next available, embedded location; and the square at the layer after that, clockwise by one interval again. The triangles are similarly treated, excepting rotated, interval by interval, in a counterclockwise manner.


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