1024 equilateral minimal stick candidate (12 vertices)

-3.791775 -4.362625 0.657719
-3.831214 3.201133 -1.947661
-0.095863 -2.248318 2.563506
3.107795 4.159184 -0.997461
-4.560500 2.317724 0.346517
-1.906889 -5.203753 -0.274559
1.211977 1.387496 3.016051
2.470825 -3.135170 -3.461664
3.153589 -0.563537 4.082906
1.761993 -0.500511 -3.794878
-0.854839 5.859725 0.291634
3.334899 -0.911347 -0.482106