Note, the coordinates for the Koch snowflake01 script, are not the corners of an equilateral triangle, so it is not symmetric.
(If the triangle is pointed up, a different pattern occurs.).

Using coordinates of a 3 sided MoI polygon, mirrored to point down, will yield a symmetric snowflake.
For example, (7.5, 2.0096189...) (0, 15) (15,15), where 2.0096189 is 15 minus sqrt(3)*15 / 2.
- Brian