I'm not sure I would use 'wedges'. Initially it looks like an efficient use of wood - but when you ask about joining them, then you see the issue. I don't think you have enough thickness in the recessed portion for any kind of joint. You could reinforce the center on the bottom of the top- but then you will again wonder how the join it. I guess you could use nails or screws. (I don't like using either.)
So you might want to try another approach. I made a similair type table two months ago and used 1 X 4's for the outside and a sheet of plywood for the recessed center. You can determine the required depth of the recessed center and either have a dado or rabbet to hold the plywood. Just a suggestion...
You could use spline joints to join the triangular pieces but wood movment would still be an issue. I made a lazy susan 13 inches in dia. with a 4 piece pie sections with spline joints which opened up after one winters heating season so for your situation I would use a plywood base and a picture frame boarder to make the top and avoid any wood movment problems.
and enter the wood species (I used African Mahogany) and a width of 13 inches and start with a moisture content of 12% and put the wood into an environment where the moisture content shrinks to 8%, the wood will shrink to 12.91 inches. And if the moisture content goes up to 16%, the wood will expand to a width of 13.09 inches.
I think this kind of moisture content change INDOORS would be pretty dramatic and would expect less movement in actual practice, but I would definitely bow to other's experience.
The "typical moisture content of 12%" comes from the USDA Wood Handbook which can be downloaded all, or in part at:
Consider this: how confident are you in yourself and your tools that would make 4 wedges come out accurate in every respect so you wouldn't have to do further trimming and fidgeting to get them as square as cutting one piece of wood twice to get a true square? I'd say laminating a "picture frame" type piece of mahogany over a 13" square piece of solid wood is a good idea. The wood movement in a mitered frame is equal in all 4 directions. There was an articl recently that described the amount of wood movement as a percentage of overall length that was very interesting. For a table your size, the movement was less than 1/32", if I remember correctly.
I have this self-created problem. I'd like to build a small square end table (13" square) with a recessed area for some tiles (loose so they can be swapped out)
I've got a sketch here of what I think I want to do. The 4 wedges will be one piece with a recessed area to hold the tile.
The plan is to make this out of mahogany.
1) wood movement. Is this going to lead to bad juju set up like this?
2) how do I join it? biscuit? spline? nothing?
3) is there a better way? (like a separate picture frame like border over a solid piece of wood on the bottom).
Note: the first two pictures, top to bottom, show the sample woods I bought to match: mahogany, walnut, oak, the bottom is the side of the table. The remaining 3 pictures are of the wood in question...