If you fold the legs over one another and sew the holes shut, you get Alexander’s Horned Sphere, which is topologically a sphere and which looks like a cursed artifact:
ALT
Showing this to my bottom surgeon at the consult
Alexander’s Horned Sphere is topologically a sphere, but its outside is
not topologically the outside of a sphere! If you put a loop through between its handles, you cannot contract it to a point without touching the sphere (or coming arbitrarily close to it).
ALT
