DejMar
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DejMar's post in 3D Connect the Dots was marked as the answer
It appears the shortest overall length of spinneret thread would be ≈ 6.196152 meters.
The red lines in Plainglazed figure would each be √3/3 meters in length, the green lines would each be √3/6 meters in length, and the central yellow line would be (1 - √3/3) meters in length. This should total (3 + 9√3)/3 meters.
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DejMar's post in Ascending anagrams was marked as the answer
As the game involved was Scrabble, the first set has the highest point value, though the second set has the best chance of hooking for a high score.