Well, I went back to the original patent of the S-trap. Then Mr. Crapper invented the U-trap or modern P-trap which added the waste arm. Now, I do believe and unvented p-trap will perform very similar to an unvented s-trap. But, until you show me where an s-trap has the waste arm extension in code, then we are both standing in the same place. And I truly want the correct answer.
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Guys like us rely on accuracy. Daniel too.
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Too bad he didn’t invent the toilet
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Maybe he just beat to a different drum trap….oh here we go!
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He was very instrumental in toilet improvements
Wikipedia excerpt:
Thomas Crapper (baptised 28 September 1836; died 27 January 1910) was an English businessman and plumber. He founded Thomas Crapper & Co in London, a sanitary equipment company. Crapper held nine patents, three of them for water closet improvements such as the floating ballcock.
He improved the S-bend plumbing trap in 1880 by inventing the U-bend. The firm’s lavatorial equipment was manufactured at premises in nearby Marlborough Road (now Draycott Avenue). The company owned the world’s first bath, toilet and sink showroom in King’s Road.
Crapper was noted for the quality of his products and received several royal warrants. - Retrieved 2021/12/16 original source: Thomas Crapper - Wikipedia
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What……s bend?
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Times have changed.
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Apparently wiki is full of sh*t 
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I guess that IS why it’s called the crapper. Sounds better than the Cummings! 
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Are we really going to just leave this one alone? I’m sure someone has something to add here.
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I’m sure Larry or Jeffery will be along shortly with a reply for ballcock and cummings
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Well, if your ballcock has an s-bend then Cummings at the Crapper might not be as fun, not to mention that your p-will be trapped.
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Unfortunately, from just looking further into it. The article you provided is wrong and a combination waste and vent system cannot be used on a kitchen island sink in the configuration on the picture from fine home building and from the picture posted by gregory.
To make it work, the piping starting just after the tailpiece of the sink must be over sized compared to the tailpiece and go straight into the floor area below into a similarly oversized P-trap and horizontal pipe, which should be vented somewhere down the line. However, this also runs into another problem. For a fixture trap, the vertical height from the outlet of the sink to the trap weir of the p-trap cannot exceed 24 inches(1001.2 UPC and 1002.1 IPC). So practically, only a short stubby sink can be installed if using the combination waste and vent system, which is not going to work for a kitchen island.
This is a rarely used and fairly new system in residential, and it sounds too good to be true as well. As the piping gets clogged, the venting space can get blocked and the system can fail. But then again that would be in a clog situation, and any other wet vents could get clogged as well. I guess from less likely to more likely to clog vents you’d have dry vent, vertical wet vent, horizontal wet vent(combo waste and vent). Please read the relevant sections and see if what I’m saying makes sense.
In 910.5 from the 2021 UPC
In 915.2 from the 2021 IPC
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I also agree I see no S-trap either. The main drain line is oversized and is most likely vented. As the OP has mentioned it drained with no problem. I may make note in my report that even though the island sink drain appear to drain properly, there was no visible drain vent observed.
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What you’re saying Yu does make sense, and IMO the best option in this scenario would be the addition of an AAV, but different jurisdictions have different rules so what makes sense to us home inspectors as a better option may not be the only allowable and cheapest way for a builder to do it.
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You’re not going to find everything in a code book, therefore we need to apply some logic to what IS in the code books and revisit the history.
First there was an S-TRAP, we didn’t have p-traps yet, the s-traps didn’t have any length to the trap arm, it was a curve:
Then we realized some of them, under certain conditions, would siphon the trap seal dry, so we started to vent them and this created a problematic crown vent. We learned that the crown vent would get clogged due to being too close to the trap’s weir and become useless:
To fix the crown venting problem we took the s-trap and added a trap arm to it, thus creating a trap that looked like a letter P and therefore a P-TRAP:
At this point we no longer call it an S-TRAP, and not because it has a vent! we didn’t call it a p-trap right after adding a crown vent to it. We first had to add the trap arm to fix the crown venting. So how can we then call a p-trap an s-trap by simply removing its vent as pictured in the OP’s pic? We cannot, we would first have to remove the trap arm and turn it back into a curve, making it look like a letter S, thus an S-TRAP.
Now, this is not to say a p-trap without a vent will not siphon the seal dry just like an unvented s-trap would, but that doesn’t mean it becomes an s-trap just because it can siphon the water seal out of the trap.
If this doesn’t make sense to you, well, nothing will 
Perhaps they will put it in the code books one of these days
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Remember the 5’ foot rule of waste stacks.
Plumbing Vent Distances & Routing Codes
So, poor venting would not siphon an ‘s’ trap dry in a newer home then? 
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