The best replacement for regular polygons is irregular polygons.

The best alternatives to regular polygons are rated as following:
★★★★★  irregular polygons
★★★  not regular polygons
★  non polygons
★  not polygons
★  polygons

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No companions for regular polygons have been suggested so far.
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Google Trends

Scale is based on the average worldwide traffic of regular polygons in all years. Click on graph for more.
regular polygons
irregular polygons
not regular polygons