72 equilateral minimal stick candidate (9 vertices)

-5.553629 0.100578 1.695456
2.342923 -1.106831 1.263454
-2.304295 3.275726 -3.552826
3.041302 -2.489015 -2.072166
-0.040013 4.170293 1.115172
-1.235482 -3.656937 2.257681
2.535450 2.781431 -0.628057
-1.140181 -4.036907 -2.628059
2.353925 0.961663 2.549347