| 3. |  |
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A = 1/2 = .500 Trivial. One of an infinite family of solutions. Symmetric about a diagonal. |
| 4. |  |
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A = 1/2 = .500 Trivial. Completely symmetric. |
| 5. |  |
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A = √3 / 9 = .192+ Proved optimal by Yang Lu, Zhang Jingzhong, and Zeng Zhenbing, 1991. Symmetric about a diagonal. |
| 6. |  |
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A = 1/8 = .125 Proved optimal by A. Dress, L. Yang, and Z. B. Zeng, 1995. One of an infinite family of solutions. Vertically and horizontally symmetric. |
| 7. |  |
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A = .0838+ Found by F. Comellas and J. Yebra, December 2001. Proved optimal by Zhenbing Chen and Liangyu Chen, 2011. Not symmetric. |
| 8. |  |
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A = (√13–1) / 36 = .0723+ Found by F. Comellas and J. Yebra, December 2001. Proved optimal by L. Dehbi and Z. Zeng in 2022. 180o Rotationally symmetric. |
| 9. |  |
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A = (9√65–55) / 320 = .0548+ Found by F. Comellas and J. Yebra, December 2001. Proved optimal by Nathan Sudermann-Merx in March 2026. Symmetric about a diagonal. |
| 10. |  |
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A = .0465+ Found by F. Comellas and J. Yebra, December 2001. Symmetric about both diagonals. |
| 11. |  |
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A = 1/27 = .0370+ Found by Michael Goldberg, 1972. Horizontally symmetric. |
| 12. |  |
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A = .0325+ Found by F. Comellas and J. Yebra, December 2001. Completely symmetric. |
| 13. |  |
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A = .0270+ Found by Peter Karpov, August 2011. Not symmetric. |
| 14. |  |
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A = .0243+ Found by Mark Beyleveld, August 2006. Symmetries of a rectangle. |
| 15. |  |
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A = .0211+ Found by Peter Karpov, August 2011. Not symmetric. |
| 16. |  |
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A = 7 / 341 = .0205+ Found by Mark Beyleveld, August 2006. 180o Rotationally symmetric. |
| 17. |  |
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 |
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A = .016481+ Found by Tej Stead, July 2026. Not symmetric. |
| 18. |  |
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 |
 |
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A = .014432+ Found by Tej Stead, July 2026. Not symmetric. |
| 19. |  |
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A = .012677+ Found by Tej Stead, July 2026. Not symmetric. |
| 20. |  |
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A = .010856+ Found by Tej Stead, July 2026. Not symmetric. |
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More information is available at Mathworld.