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Apparently, using the magic of topology, and specifically gluing/identification diagrams (required knowledge for this page), one can transform a hyperbolic stop sign into pants!
First, let's inspect our stop sign.
There's 8 sides, as normal. In my model here, I made two sides yellow, and two sides blue. If we match up the colors together and sew them up, we get a surface with three holes: one on the top, and one on either side.
Here, we see that the holes are where the red sides are, since the yellow and blue sides are fully attached. So, two red sides become the top hole, and the other two red sides connect to themselves to become holes half as big.
Now, recall pants. They have three holes too, dont they? A big one on top for a waist, and two smaller ones for legs? Isn't that what we have here? Why am I asking questions?
So, with some imagination, this folded up stop sign is kind of like pants. But honestly, not really, since all the proportions are off.
But! If we make a hyperbolic octagon, we can fix this!
Behold: an octagon. Well, it's not quite as neat as our stop sign. But, the same principles apply: if you count them up, there are 8 sides, with 2 marked yellow and 2 marks red, just like the model from earlier. When we go ahead and identify the colors together, we get...
Pants! Look, they actually stand up, and look somewhat reasonable! Actually, the curvature seems to make them bell bottoms, so that's fun.