It has possibilities, but I'm not sure if I like it well enough to design an outer border that would bring it all together. Before you go shooting yourself for being slow, this doily is just a photo image copied and pasted. I wanted to see what the negative space would look like where they join. I like the join, but I'm not crazy about the outer edge. I think maybe it would need something to bring it all together and connect the outer points. I had no idea that the points were going to look so square, but it does make for an interesting design element.
Now there's an idea for an eight person round robin. The first person does a snowflake, the next 6 just make and attach a repeat of the first snowflake, and the last person has to do an outer round to finish it off before sending it home. So everyone would make 7 snowflakes, all different, and one round to finish off a doily, and everyone ends up with a doily which is mostly their own design.