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Use the Percentage Circle for the octagon grid, marking off 8 equidistant points on the circumference. Start at 0, then count by twelve and a half to 12.5, 25, 27.5, 50, 62.5, 75, and 87.5. You can later choose to inscribe regular polygons with 5, 10, and 20 points.
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Here's a Percentage Circle for you to view or print out.
Picture
Sketch (202K) (Geometer's Sketchpad 3.0)Chord length commensurate with 200, as marked along the % circumference, can be rotated. Here's a sampling of chord configurations of twenty points on the percentage circle. A sketch (139K) is also available for viewing and printing out.
If we count five starting points on the circumference, there are still more ways of inventing grids.
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The number of sides of the initial pair of inscribed polygons gives the grid its uniqueness; these grids are based on overlapping pentagons.
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