Help with conceptualising a problem.

Question

I've been considering shapes formed when we take $n$-tuple such as $\{0,1,2\}$ and plot all permutations forming a shape (for $n=2$ its a line, for $n=3$ it's a hexagon). However I'm having trouble trying to understand the plot for $n=4$, mainly because it's in 4D and that's hard to plot. I feel as though it's just going to make $n!$-polygon. I'm in high school so I don't really have a rigorous mathematical training hence why I'm looking for some guidance in how to approach such problems.