If you want to build a house, it’s easy: You pay your builder, and you give him the land. All he does is build the house on that particular spot of land.

A little bit more complicated, but not too bad. More complicated still if we’re making a 3-dimensional object like say a vase or something round like a CD. We have to make sure the vase is a whole number of turns, not “one face”, but “two faces” or “3 faces”. Then most of the rest of it is as in 1.

Oh yeah, and if you want to make it a cylinder that goes all the way around, you need to give your builder a cylinder that he can unwind. Depending on what sort of object you’re trying to produce, this might involve giving him some extra materials like rubber bands or pieces of string. Funkishus

But if you want to make a cube, it’s almost as easy as for a vase. The only thing is you have to give your builder his own special glassblower’s shape, and [unlike the previous examples] this doesn’t limit him to the size of the object he’s trying to make—it only limits the size of his “work space”. What remains is a search problem where your builder has to find all the corners and sides of this shape so he can start making it. Moderne hus

This problem is the same as the one we had before: “What’s the largest possible cube that can be made out of this collection of [specific] blocks?” Your builder has to arrange these blocks so that they form a cube; your builder’s shape must somehow correspond to a cube.

In neither case are we asking for an algorithm. We’re just trying to guess “what shape is he going to make”. Whatever shape he makes, it will be bigger than some specific shape in the limit of time allowed. There’s nothing to make our lives easier, except that the result has a lot of symmetry: In one way or another, it’s always a cube.