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Thanks to Durban, whose comment I somehow missed earlier, and to others who've commented since. Yes, I was assuming that the preamble, "All items are formed of straight lines joining cell centres" meant that a line would exit one cell from the centre and enter a neighbouring cell to the centre, etc., the method I used for outlining the other shapes.

Bank Holiday greetings to all. Came on at request of Mr Rainbeaux, who thanks you for the nudges about positioning the final object. He'd also assumed cell centres all round and we were getting a little heated working out the trigonometry. He would also appreciate tips on parsing of 37a and 23d - he has correct answers according to definitions and necessary clashing cell, but can't fully parse them.
Sorry Meursalt, we take your point - unfortunately we rarely have anything to contribute.

37 pen - nills
23 gram - (so)matic

Thanks, unclued, all squared away now.

Started this today so am behind all of you on here.
I seem to have finished, but I have 8 clashes and only 4 shapes. Can't see the Q one, although it's obvious where it starts. Can someone tell me if 8 is correct, and how many letters in the Q. I have 4 words that have 2 clashes and 6 that have one.

Ah, just found the Q and got the rhombus in. Just a bit puzzled by someone saying that 6 clashes was correct.

Hi xij,

There are six clashes in all. Six answers contain a single blank cell and three answers contain two blank cells. You need two blank cells for the S item and one blank cell for each of the other four items.

The Q item consists of 13 cells containing the letters making up the name of the item and one blank cell.

Thanks Wintonian. That information made me check every answer. I found that I had bedroom for 45, which made sense at the time, and 2 as a clash answer, getting the U's mixed up, but have now seen the error. I now have 6 empty cells.
Still don't see the wordplay for 1a or 37, but apart from that, a very fair puzzle.

1ac is BUFO with an extra F.

37 is pennills (Welsh form of verse) minus 'pen'.