You have a cube with an edge length of s, and an elastic rubber band. The idea is to stretch the band around the cube so that half the area of the surface of the cube is below the band, and half the area of the of the cube above it; and every bit of the rubber band is at the same height, that is, it is all on one horizontal plane.
How long is the band? Is it constant or does it vary depending on the orientation of the cube?
If the cube is on a face, the situation is simple enough.
The length of the band is 4s, of course.
But what if the cube stands on an edge?
What if it stands on one of its points?
Is there a generic solution of some sort?
What is the shortest / longest possible length of the band?