thanks Al. I get it now. Still clueless on why they would call it a die and not a cast? The words makes no sense to me...
Well as they say, the die is cast...but seriously:
A die is an object(s) used to shape material in a variety of ways, a cast is the product of a mold, and not all dies are true molds.
The dies that make archbacks would be in the category of what they used to make car fenders with, the dies that make wire by pulling metal rods through successively smaller holes are yet another type.
Die
casting refers to a molding process in which liquid metal is injected under pressure into a mold which is actually made of tool steel dies as the halves of the mold. The process gives extreme dimensional consistency between all the castings.
In our case the "die block" would be one half of the die set that has the shape of the outward bulge of the archback, the "punch" would be the mating half that pushes the wood laminate sheet onto the "bowl" of the block,
It could be the other way round, it's just that the part that's stationary and secures the sheet is the block, and the moving/cutting part is the punch.
I don't know whether the outline is punched out of the sheet at the same time as the arch is formed, but it's possible, and thinking about it, it would probably be more accurate and less labor intensive if it was, and I assume they all need to get finished down to final fit by hand in any case.
https://en.m.wikipedia.org/wiki/Die_(manufacturing)