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For some reason, all the Duplo bricks that exist out there have holes in their studs. I haven't seen a Duplo brick that doesn't have holes in the studs, and I doubt such thing even exists.

System bricks can actually connect to Duplo bricks with these holes, but is that the only reason for the holes? Is there is a Duplo brick that doesn't have holes in its studs (if yes then please point it out in the comments or in your answer)?

What are the other reasons for Duplo bricks to have holes in their studs, if any?

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Plastic molds are designed to have an even thickness wherever possible (I think it helps with cooling), so a having a hole in the stud made sense to keep the brick's walls consistently thin. The hole could have been placed on the underside of the brick, but putting it on top had the obvious advantage of being compatibile with standard bricks.

Interestingly, DUPLO baseplates have their holes on the underside rather than the top. I believe this is because baseplates are vacuum formed instead of injection molded.

DUPLO baseplate

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    Baseplates, at least for regular sized LEGO bricks, are made using vacuum forming/moulding: "Vacuum molds work like this: a sheet of plastic is placed inside a molding machine, and two radiant heaters pass above and below the sheet, heating it until it is soft. The sheet is then subjected to vacuum, i.e. it is “sucked” down into the mold and forms the familiar LEGO studs." – Alex Jun 28 at 15:27
  • @Alex Thanks I'll amend my answer. – Pubby Jun 28 at 19:13
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The holes are necessary so that regular system bricks can fit on the Duplo bricks. The ratio is 2:1 in both dimensions, so you need four 2x4 system bricks to cover one 2x4 Duplo brick. This is an intended feature of the Duplo bricks and was decades ago even advertised in catalogues.

Regarding the baseplates: Some people claim that TLC does not want people to use the comparably cheap and large Duplo baseplates for their large Lego system diorama designs which would be possible if the studs were hollow...

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