This may be an already solved question. Let us be given with l lengths AB , BC , … , LM , l being l ≥ 3. What is the condition that we can construct a figure with them? And what is the least dimension n required to do so? Is there a general solution for this question?
My question is not restricted to polygons but also includes polyeders, cells, etc.
If by "figure" you mean a polygon where $\,M \equiv A\,$ then the necessary and sufficient condition is $\,AB+BC+\ldots+LM \ge 2 \cdot \max(AB, BC, \ldots , LM)\,$, which follows from the triangle inequality. This holds in any dimension $\,n \ge 2\,$, and such a polygon can in fact be constructed in a $2$-dimensional subspace of the $n$-dimensional space once the condition is satisfied.