A tripod is the most stable structure I know of and I had questioned why most tables I see are made with four legs instead of 3. building this table showed me the difficulties in free-handing a three legged table and why most people build then with 4 (though building a jig of some form would make it just as easy).
I'll try to explain how to make this as best my ability to do so, though ask questions if something is unclear.
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Step 1: Break Down Your Palate
I started off with a square pallet and I was able to complete the table with just one. It comprised of three 2x4s and cross members. The first step is to break it down, I did this by pulling out all the nails in a way that I could re-use them. You could also use a sawzall or hack saw to cut through all the nails, but you'll need your own for assembling the table.
Step 2: Construct the Sides
Take the three 2x4s and lay them down. These will be the table legs.
If you want a shorter table then cut these down to size, though mine looked right so I left them as they were.
Cut three of your boards in half. These will be used on the sides as braces to stabilize the table and prevent twisting.
Attach two boards to each leg. The first board is an inch from the top and the second is roughly centered. Do this for all three legs.
Step 3: Assemble Your Three Sides Into a Tripod
Step 4: Design Your Table Top
At the end I took 3 half lengths to make the top. I nailed a piece spanning each leg and trimmed them to fit interlockingly like a puzzle. I took two pieces that got trimmed off and cut them to fit inside. These just happened to press fit. If you'd like you can angle the edges to fit them in if theyre loose, or better yet just glue them in. Maybe even glue four boards together and cut out a circle to place on top (just dont be a square and use a four cornered topper).
With that the table is completed! I have had mine for the whole summer. It sits next to my aquarium holding important fish stuff.
I hope you enjoyed, please show me some pictures if you decide to make one yourself.