Polygon construction

In the boundary transition (n > oo), the polygon—constructed by the mirrors—becomes a circle with radius R, and the difference of the times needed to circle around the disk in the opposite direction is thus... 

If what is required is a polygon with points actually on the limit curve, then these can be constructed by multiplying the polygon constructed in the previous paragraphs by the unit row eigenvector. 

Figure 21. Classification scheme for vertices in the polygon construction. The fourth column gives the tiling charge, as defined in the text.

Fig. 5.3. A two-dimensional system with its network of Voronoi polygons. Heavy lines boundaries of the Voronoi polygons. Light lines the dual network of polygons, constructed by lines kj connecting pairs of particles which contribute a boundary for the Voronoi polygons of i and j.

Q Explain how to construct the molecular orbitals of a conjugated cyclic system similar to benzene and cyclobutadiene. Use the polygon rule to draw the energy diagram, and fill in the electrons to show whether a given compound or ion is aromatic or antiaromatic. 

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