Makes use of symmetry by having the snowflake rotated 9 times and the other half end up in the same place.

The equilibrium shows a shortcut to work out the geometry of these rotations fast. Each of equilibrium marks the handoff point or in other words the center of snowflake when the next arm grabs it. Since each of arm 1, 2, and 3 rotate the snowflake 3 times, their two handoff points are three rotations away, which then mean that the arm base must be the middle point of their two handoff points. With that I can derive arm 3's placement as I decide how arm 1 hands off to arm 2.