IKR?
Vomitorium.
The nearby football stadium has a couple of these.
I’ve always wanted to design a house with one, just to use it in conversation…
Analemmata?
Proskenion or hyposkenion, with skene being the shorter general term?
Here is a Mini-Dictionary of Garden Structures and Plant Forms which doesn’t include anything that meets your criteria.
That was my first thought. A peristylium/peristyle or a hypostyle.
I’m sorry I haven’t replied earlier, but I now think that tetrapylon was probably it.
Many thanks to all who joined in!