The number of elements that are capable of forming a polymer just by themselves and without the assistance of other elements is very small. A large part of this is due to most of the periodic table being made of metals, elements that not capable of forming polymers (at least as far as we currently understand). Throw out the noble gases and you only have a very tiny wedge of the table for consideration, consisting of the metalloids, the nonmetals and the halogens - a total of 16 out of the 92 naturally occurring elements.
Boron, carbon, silicon and germanium are all known to form covalent network solids, which I would consider to be polymers (although others certainly would be entitled to disagree). Sulfur can polymerize under high pressure, but that is it. 5 elements.
Now a new report (Open Access) has found that iodine can polymerize. Not as polyiodine, but as polyiodide (the anion). Oligomeric forms of iodide are already known. I mentioned I3- (triiodide) many times in my general chemistry class last year (it's a good one for drawing a Lewis structure) and higher iodides such as I5- and I7- are known to exist, but now comes proof of In-.
The unusual aspect of the polymer is that it doesn't exist by itself, but instead is supported by a pyrroloperylene crystal structure, with the entire iodide-pyrroloperylene complex being crystalline as well. That crystallinity is what made it possible to clearly identify the polymeric nature of the iodide. (Ferreting out the structure of an amorphous polymer is a whole new level of hurt.)
While the iodide-pyrroloperylene complex is of interest to the researchers because of its electrical conductivity, they also realize that polyiodide may finally crack a chemical mystery that is nearly 200 years old: the nature of iodine in the blue solution that form when iodine is added to starch (an elementary school favorite). Polyiodide has been suggested as a possible form, but without any proof (the iodine-starch complex is amorphous...), it was just a suggestion. This new research doesn't prove that the of iodine in a starch complex is polyiodide, but it does provide support for what could only be previously considered as just a hypothesis.
And it gives us a 6th polymeric element.