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Many(all?) of the inverted slope pieces have solid studs and hollow studs( e.g. 3665) and a void around the stud. This(void & hollow) looks very inelegant, is it really that difficult to make solid studs with finished surfaces on these pieces? What's the material/cost/grip/aesthetic trade-off?

If lego decided to fill the stud and void of 3665 (i.e solid piece except for anti-stud), what would be the downside (apart from plastic, which is trivial)

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Because of the way ABS plastic injection molding works, it is important that parts have a uniform thickness throughout, and don't just have a large section completely filled with solid plastic. This page explains a little about that:

As the plastic solidifies in the mold, it freezes from the outside (near the mold surface) toward the inside. In thick sections, this results in inward pulling stresses (due to contraction) that can cause sink marks in the outer surfaces of the part. In addition, because thinner sections will freeze faster than thicker sections, there is also the possibility of stresses building up between thick and thin sections, resulting in part warpage.

molding errors

The reason that the stud is open is because that area of the part couldn't be reached from the bottom as usual due to the closed slope underneath. The constraint of uniform thickness forces either the top or bottom of a stud to be open. This is the same basic reason that the studs on Technic beams are open as well.

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Cost of the brick would raise by 10-20% of the extra material needed, I don't expect the mould to be more expensive.

But I think the main reason is the production proces itself. ABS is processed at around 200C (don't know temp used at LEGO). After filling the mould the whole brick must cool down again. To keep the brick shape stable, this process must happen at the same rate through the brick. If parts of the brick are thicker than others this takes more time to cool, which can cause the brick to deform during production, so it doesn't meet its tight tolerance spec.

I can't really come up with a Lego brick shape that is locally much thicker than the rest of the part.

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