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I have a full grid, the unclued individual and the three cell pairs for under whose name the quotation appears. No got a scooby-doo of the 28 cells representing the geometrical structure as I don't know what it is.

Same! Came here for some enlightenment…

I can see a 10 letter word for a geometrical shape in the completed grid plus two other words that complete the shape (the words are referred to in the wiki article for the person). But these only add up to 20 characters and I can't see any other candidates.

When I saw "geometrical construction" I thought this was going to be way outside my comfort zone. Then it dawned on me that the letter Q was not sitting in an unchecked cell for the good of its health. I also spotted the 3 cell-pairs which enabled me to consult the ODQ, without which I wouldn't have been able to finish.
The whole thing brought back memories of a show I'd enjoyed enormously at the Criterion Theatre in 1969!

Aha, found the quote and now have the remaining eight characters.

Gosh you are all way ahead of me, so please will you help me with 27a? On Sabbath, long for some directions (5) I have ??D?S also 35a please: kids computer image largely entertaining adult (4) I have ? a?e

Jogamel, a hint for 35 A.

The clue, importantly, has Kid's, NOT your Kids...
There's a four word term.abbreviation for an everyday computer image. It loses the last letter (largely) and gets an abbreviation, for adult put inside. The definition is, the definition's the first word in the clue.