My second attempt at pouring a tile grinding tool went much better.
I went out the next day and bought a new tile mat. The salewoman in the tile store, as my wife likes to say, looked at me like I had nine heads when I told her I wanted a square foot of tiles that were "sort of small, and any color" to grind a telescope mirror with. She was friendly and helpful, but my wife said she was clearly humouring me.
Unfortunately, the only tile mat they had available had tiles about 2.5 inches on a side. This was rather larger than I wanted, and I wasn't sure it would work out OK. You see, when you make the tool at first, the tiles form a sector of a polyhedron that is inscribed inside the mirror surface. The corners touch the mirror and the side form chords that go away from the mirror surface then back towards it at the next corner.
I was concerned that with such large tiles it would take a long time until I had ground down the corners sufficiently that the entire tiles would come into contact. In the end it worked out OK, I had nearly complete contact by the end of rough grinding.
I wasn't worried about not having enough channels in the lap. While one reason we use small tiles rather than one large single ceramic tiles is that the channels help distribute the abrasive and water, most of my previous work had been done on unchannelled plate glass tools. These worked fine, and were the standard way of doing things for many years, so I wasn't worried about not having too few channels.
I made the tool in a similar fashion as my previous attempt, with the exception that I didn't cover the mirror in plastic, just thickly applied petroleum jelly. I pressed the tiles down into the jelly so they would stay in place. Also, I mixed the dental stone much thicker.
I poured a smaller quantity of water into the mixing container and gradually poured in dental stone, mixing it with my hand, until it was about the consistency of thick yogurt. Towards the end I had to find and break up clumps. When I poured the stone into the mold it didn't want to pour on its own, instead I had to scoop it in with my hand and pat it down to get it to lie flat. Mel Bartels on the ATM list said it sounded like I had mixed it about right.
I probed the stone all over with a nail to push down any tiles that may have risen up, but I think with this thicker mixture this wasn't really necessary. As a testament to the thickness of the mixture I had trouble getting the nail holes to close up.
I had less mixture this time so that when I poured it all the tool came to about 1.25 inch thick (including the tile). I thought this would be too thin but a couple people on the list said this was fine, and cautioned against too thick a tool - for example, a thick tool would be very heavy and dangerous to the mirror if it was dropped on it, as happened to one poor fellow. In practice the tool seems plenty strong and feels about right when grinding with it.
The thicker mixture set up much quicker.
Before the stone was completely set I stripped the mold sides off and trimmed the "antibevel" with a putty knife. My wife helped with this. Some stone had slipped all the way down the side; I would have done well to bind the sides to the mirror with a tightly wrapped string or wire.
Once the stone was trimmed away from the mirror sides, the tool slid off easily sideways. Don't try to pull it straight off, as it will be held firmly by the vacuum formed by the petroleum jelly. It seemed to be fine to just use petroleum jelly as a release agent, but I would worry for much larger mirrors. Of course one must be careful that the entire mirror face is thoroughly coated, so that there isn't a spot of adhesion.
Also we trimmed the stone from between the tiles with the putty knife to form channels. I would have done better I think to use a fine wire brush as someone else suggests on their page about tile tools. The problem was that in places the putty knife scored narrow channels where grit gets in and is hard to clean out when cleaning the tool in preparation for going to a finer grade of abrasive.
Also something troublesome that I didn't notice was that some bubbles had broken the surface and formed repositories for grit. The think to do would have been to open them up so the grit would easily wash out. What I must do instead is carefully wash each one out with a spray bottle when changing abrasive grades.
I wrapped the set tool in wet paper towels and left it overnight in a plastic bag to cure. After a while it got noticeably warm from the curing reaction.