Let $n\geq 3$, and consider an $n$-gon, not necessarily convex. What is the minimum number of distinct lines that are formed by sides of the $n$-gon?
When $n=3,4,5$ the answer is $3,4,5$ respectively. For $n=6$ we can save one line, for example if we draw the "V-shaped" $6$-gon so that the two sides at the top of the V form the same line. For larger $n$ we should be able to halve the number of distinct lines by forming a "star shape" so that opposite sides of the star form the same line. But can we do better?
Can we do better? Yes:
This figure has 28 edges forming 12 lines. If you count this as "2 indents on each side" then the generalisation to "$k$ indents per side" has $8k+12$ edges forming $2k+8$ lines, approaching asymptotically 4 edges per line.
Are there better configurations? I'd conjecture almost certainly :-).
Edit: In fact we can get the ratio arbitrarily low. In these figures with $k$ 'towers' and $k$ 'tiers' ($k \ge 2$) there are $8k^2$ edges in $6k+2$ lines ($2k+2$ horizontal and $4k$ vertical), giving at least $k$ edges per line.