I am assuming that a polygon is defined as a 2-dimensional polytope.
In that case, a 1-dimensional polytope will be a connected union of line segments. In other words, it is a physical realization of a graph.
Is there a short professional term for this concept?
I am Guy Inchbald. In modern polytope theory, a 1-dimensional polytope is just a single closed line segment, meaning the end points are included as its vertices. A full-blown graph is effectively a polyhedron, as it has the same combinatorial structure (Search for Grünbaum on "Polyhedra as graphs, graphs as polyhedra"). There is indeed no consensus yet on what to call the 1-polytope. Amazingly, the first time that any term was formally used was not until 2018, in Prof. Norman Johnson's "Geometries and Transformations" (Cambridge University Press). He used "dion". This was some years after a few people had used "dyad" informally, which I thought unsuitable because it was used for other things and also begged the question, two of what? So I had proposed "ditelon". Johnson contracted it "dion" for his book, which I also find unsuitable because it begs the same question. A "ditelon" it a two-ended thing, "telos" being the end of say a rope, in the same way that a polygon has "many corners" and a polyhedron has "many seats" or faces. You know what you are talking about. Who am I? Nobody very much, I have just published a few papers on polyhedra. You can find a fuller explanation of the issue on my web site at http://www.steelpillow.com/polyhedra/ditela.html