Take the little box above as an example. This piece of rhyolite had jagged edges so the choice to round the edges softened the top. The box was shaped to conform to the top.
If you approach box-making like an engineer you would likely end up with a different product. Engineers look for economy, utility, and ease of manufacture. Box-making from an arts/crafts point of view requires being flexible with the materials and using them to dictate how to proceed.
Cutting slab widths varies with the kind of rock and its strength. This variegated piece of jasper is 1/4 thick because of its tendency to have checks that could weaken or break. The corners were sharp to the touch, so a bit of chamfer made this rock more user friendly. I generally slightly chamfer each lineal edge to a 45 degree angle to soften the feel of the lid.
In most cases, the rock demands the box. When you cut a slab you never know exactly what you are going to get, so some aspects are random. I find the biggest and best view of the slab and then trim. The box building matches the rock.
Sometimes the box comes first. In the case of this composite box above, I had a certain size in mind for a particular purpose. The overall box size was 12"x12"x4". I could never have cut an 11" slab on my 16" saw, so conformed odd pieces to fit a window-paned top. Each piece is slightly chamfered. This give a more pleasing look to the stones as set gems.
In the example above I cut into a friable piece of lovely rhyolite and it cracked into several pieces. The solution? Preserve each piece as large as I could and puzzle them together into a window pane. Since some of the pieces were thinner than others, shimming the underside of the thin ones to conform to the thick ones is a faster solution than grinding down thick rocks!
You can glue two slabs together if you carefully grind them to abut together. A good polyacrylate glue will hold the rocks together so you can make a fitted top or a supported slide top. Glued rocks will not suffice as a simple top or a slide top without support.
A fitted top or support for the slide is the best solution for a series of glued rocks.
Note how there is a base for the rocks in the upper box at left in a fitted top and there is a wooden base on the slide on the bottom box of three stones.
Some long boxes, like this 10" one at the bottom is hard to make without using more than one stone. Cutting large slabs can be tricky as they can lose integrity and crack.
If a rock is strong and can withstand flexing and mild abuse, then a slide top can be made so that the top and slide are simply rock. In the example at left, the faux jade is cut to a 1/8 inch slab and fits in the slot for the slide action.
Depending on the stone, I may chamfer the edge to a significant bevel. You can do this on a flat lap by hand although it takes some practice to keep the angle consistent. I will need to devise a jig so I can cut accurate bevels all the time without variance.
There are few boxes that I couldn't make adjustments or change some feature to adapt the stone. To me, after you find a rock, transport it home, evaluate it for cutting, slab it then polish--it is too valuable to toss! Some of the first iterations below show the evolution of how boxes have become more intricate. There are all simple, solid top boxes.
From left to right: Marbled agate, Stinkwater petrified oak, Leslie Gulch ash flow, petrified wood, Owyhee country stone, McDermitt picture stone.