Sometimes it's fun to see what a design element will look like with different points of symmetry. The following images have been drawn individually, using the Kaleidoscope Drawing Pad app on my iPad.
Here is the same idea, done with four, five, six, and eight sides:
Once I have a basic drawing, I will often need to go back and alter portions of it to increase the chance that it will be tat-able. Just glancing at the image above, I can see that the angle of the long outer chains in the square motif would be difficult to maintain. The same might go for the five sided motif. The hexagon would probably be okay to make a simple snowflake. Lastly, the octagon would need to have some alterations to enlarge the outer rings.
Let's look more closely at the octagonal drawing. As points of symmetry increase, the spacing between the outer rings gets smaller, causing them to eventually become scrunched and out of proportion with the inner rings: