Join operator for generated lists of polygons

Questions
1

I want something like the sum operator (big sigma) for join so I can produce one final list by joining the expressions at each index. Or a list comprehension that produces lists to be joined, not list elements?

I’m working on a string art activity, so I have lots of lists of polygons.

I know I can turn the code inside out (that’s how I started), but the code is much more abstract now.

I noticed some dark magic use of Sigma in discussions of list manipulation, but I haven’t been able to sort that out.

Here’s a way stripped down example:

Thanks!

2

Here’s what I came up with using list comprehension. It’s not actually joining the former list. It creates the whole list but integrating the sum and differences within using the t_sign list. merging lists of polygons | Desmos

3

Thanks, Daniel. That’s sort of what I meant by inside-out, probably better described as inlining.

If you’re curious …
I’m trying to get rid of joins in the 20s (code line numbers) and other places:

Which is driven by:

4

I’d say there’s a way, but not without going all the way back to the initial function that uses polygon(), which can’t really be manipulated in list comprehension. At least as far as I understand, you can manipulate functions of lists in list comprehension, but using the join method is just not friendly and needs to be done manually. There are lot of nested functions there that make your job pretty difficult.