Packing $13$ unit circles in an equilateral triangle

Packing 13 unit circles in an equilateral triangle

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The side length of the smallest equilateral triangle into which $13$ unit circles can be packed.

Lower bound: Unknown
Upper bound: $4+\frac{2\sqrt{6}}{3} + \frac{10\sqrt{3}}{3}$ (≈11.4065)

Updates

1993-12 Upper bound: $4+\frac{2\sqrt{6}}{3} + \frac{10\sqrt{3}}{3}$ (≈11.4065)
Melissen, H. (1993). Densest packings of congruent circles in an equilateral triangle. The American Mathematical Monthly, 100(10), 916-925.
[via Circles in Triangles, Erich Friedman]