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Hounds, I wouldn’t consider myself part of a super educated elite clique. I’m from Wigan 😂. But this as many other listeners was perfectly possible (albeit invariably difficult) with a chambers dictionary, chambers crossword dictionary and google by your side!

I suspect the setters must be part of some kind of super educated elite though cos it blows my mind every week how they’re able to create them!

Different themes appeal to different solvers. I don't agree that this one was especially arcane - I suppose that all solvers had the information needed to get the permutations, whereas few would have in mind the words which go in the unclued entries - I didn't. Everything could be looked up once one had done enough to know where to look.

There's one puzzle in the last few years I remember hating - it required some special knowledge of the Spice Girls. But other solvers will have enjoyed it.

Elitist? Well, the Listener is an elitist crossword, in terms of vocabulary and solving prowess. Obscure themes are ok with me so long as it's possible to do the research online.

Hounds, I too am not super educated or part of any elite clique. The Listener covers a myriad of different topics and themes and I find researching them interesting, and often educational, The end game is often the most frustrating part for me but that only compels me to crack it - after all it is part of the PUZZLE. If you hanker after difficult crosswords based on wordplay alone there are plenty of alternatives available so I would recommend trying some of those. No ne should be expected to know everything about everything but they should anticipate that further research may be necessary to complete a Listener.

I thought the theme was fine. The geometry is lower secondary school maths, the associated name and place well known and the Greek alphabet is common knowledge. The only thing I did not know was the message, but Wikipedia readily supplied that, and it was cleverly done.

What I disliked about this crossword wasn't the theme but some of the clues. I particularly dislike clues that require reading entries in Chambers for particular wording. Rather than the wordplay leading to the answer, you almost have to know the answer before you can understand the wordplay. 13 down, as previously mentioned, illustrates my point perfectly.

For me, the best setters are those who use common English meanings but in a way that challenges your interpretation. That's particularly true in wordplay where you have to identify the redundant words to be removed. In such puzzles, the parsing should be crystal clear.

I think I have finished but I am not sure what I have drawn. I have a complete grid, location, message and a shape consisting of 6 lines (one modified according to the preamble).
My only doubt is the significance of the shape. I suspect it is mathematics but I can’t find a link between that shape and any potential proprietor of the location.
I don’t want anyone to give too much away but it would help if I knew if the proprietor is the originator of the location, its more famous later occupant or someone else?

It is the originator, smithsax, and the simplest possible figure for which they are known

I am now completely stuck. I think I have permutated the extra words correctly and they give me an institution associated with kyrioi P and S. I think I have found the line which "respects the cells visited". I do not know whether I am looking for one, two, three, four or five more lines. I have tried Googling this information, but this has not produced anything which makes sense to me. I assume that I am on the right lines, but a nudge would be appreciated.

OptO, if you join the centres of all the blank cells, you should have 6 straight lines. One of them goes through 6 cells which can be read as an adjectival phrase. The 6 lines depict a 3-dimensional solid that belongs to a set of solids with similar features known by the name of the first of your kyrioi. The message is connected with what you have drawn.

Thanks both. Got there eventually. I was using “quadrilateral” as a search term when I should have used “solid”.
Another deficiency in my education exposed.

Always worth remembering that a shape can have two or three dimensions, smithsax