3. |
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A = 1 Trivial. Completely symmetric. |
4. |
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A = 1/3 = .333+ Trivial. Completely symmetric. |
5. |
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A = 3 – 2√2 = .171+ Proved by Royce Peng in 1989. One of an infinite family of solutions. Horizontally symmetric. |
6. |
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A = 1/8 = .125 Found by L. Yang, J. Z. Zhang, and Z. B. Zeng in 1991. Proved by L. Yang, J. Z. Zhang, and Z. B. Zeng in 1994. One of an infinite family of solutions. Horizontally symmetric. |
7. |
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A = 7/72 = .0972+ Found by David Cantrell, July 2006. Proved by Z. Zeng and L. Chen in 2019. 120o Rotationally symmetric. |
8. |
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A = .0677+ Found by David Cantrell in July 2006. Proved by Nathan Sudernmann-Merx in 2026. Not symmetric. |
9. |
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A = 43/784 = .0548+ Found by David Cantrell in July 2006. 120o Rotationally symmetric. |
10. |
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A = .0433+ Found by David Cantrell in June 2007. Not symmetric. |
11. |
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A = .03652+ Found by AlphaEvolve in June 2025. Reflectional symmetry. |
12. |
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A = .0310+ Found by David Cantrell in July 2006. Completely symmetric. |
13. |
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A = .0265556+ Found by Tej Stead in July 2026. Not symmetric. |
14. |
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A = .0237+ Found by David Cantrell in June 2007. Not symmetric. |
15. |
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A = .0210+ Found by David Cantrell in June 2007. 120o Rotationally symmetric. |
16. |
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A = .0179+ Found by David Cantrell in June 2007. 120o Rotationally symmetric. |
17. |
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A = .01551+ Found by Tej Stead in July 2026. Not symmetric. |
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18. |
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A = .01339+ Found by Tej Stead in July 2026. Not symmetric. |
19. |
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A = .01116+ Found by Tej Stead in July 2026. Not symmetric. |
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20. |
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A = .01010+ Found by Tej Stead in July 2026. Not symmetric. |
21. |
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A = .009468+ Found by Tej Stead in July 2026. Not symmetric. |
22. |
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A = .008538+ Found by Tej Stead in July 2026. Not symmetric. |
23. |
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A = .007748+ Found by Tej Stead in July 2026. Not symmetric. |
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24. |
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A = .006847+ Found by Tej Stead in July 2026. Not symmetric. |
25. |
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A = .006386+ Found by Tej Stead in July 2026. Not symmetric. |
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26. |
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A = .006225+ Found by Tej Stead in July 2026. Not symmetric. |
27. |
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A = .005483+ Found by Tej Stead in July 2026. Not symmetric. |
28. |
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A = .005230+ Found by Tej Stead in July 2026. Not symmetric. |
More information is available at Mathworld.