The best replacement for irregular polygons is regular polygons.

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

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

Scale is based on the average worldwide traffic of irregular polygons in all years. Click on graph for more.
irregular polygons
regular polygons
congruent polygons