Interesting image, Lon. Like your idea that it is like a puzzle, I think of the One Christian faith (Eph4:5KJV), borrowing the notion from materials science, as like a crystalline solid.You are like a kid who sees a puzzle while he is working on the middle. He sees a horse head on one end and a lion hind end on the other and throws out the lion back end and opens other boxes of puzzles until his picture makes sense.
Crystalline solids are as their name implies crystalline, in their physical atomic structure. But no crystalline solid of any appreciable size is a single crystal, but is composed of multitudinous single crystals, joining together at what are called grain boundaries. Each single crystal is composed of the same types of atoms, so that the solid is of continuous composition all throughout.
The physics of the grain boundaries unite together all the single crystals into the one crystalline solid---analogous to the aforementioned kid completing the first puzzle of the horse and the lion all the way, if I'm understanding your thought correctly. Without grain boundaries, crystalline solids couldn't exist as anything but the finest powders, and this includes metal. Metal coins, tools, pieces and parts wouldn't exist, if not for the physical interactions at the grain boundaries between many, many tiny single crystals.
FWIW.