Hi. When adding strokes to items, Illustrator considers each item as separate, by default. However there is one workaround you can try, and one that will definitely work (but will eliminate the polygons - although that might be fixable, too). There're several other methods that can be used, but I'm offering what I consider the simplest solutions.
1) Select all the polygons (you can use the selection tool to drag a rectangle around all of them and they'll all be selected. Now, I haven't tried this on something like yours, but it may work. Go to the Object menu> Compound Path> Make. Then, try the stroke again. Compound path makes Illustrator "think" of many objects as one object, while maintaining all the individual components of the compound object separate (you can see it in the layers panel)
2) OR, you can make Illustrator combine all the shapes into one total shape. This will eliminate the individual polygons, but you'll have a single shape you can stroke. You could use the Pathfinder>Unite button, but I'm going to tell you a simpler way...
There's a tool in the toolbar that looks like a trident - it's called the Shape Builder tool (hover for tooltips to find the name). With all shapes selected, you can use the Shape Builder to drag from one polygon to the next, to the next. Each drag will combine those shapes into one, cohesive shape. You'll end up with one whole shape - no polygons, which you can stroke. NOW, what I'd do if I wanted to KEEP the polygons is to do exactly what I just described on a duplicate layer above the original. Lock the original layer so you can't touch it, and run the shape builder on the layer above. Stroke THAT layer and leave the fill empty. That way, the stroke appears to be around the polygons, but you can still manipulate the polygons on the original layer after you've unlocked it.
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