How much load will this triangle have to carry? For a side table, even with a stone top, I doubt it would be more than 50 pounds. All I could find on line for axial compressive load (vertical load on the edge of the plywood), is 11 pounds per square inch of plywood.
So if the triangle is about 10” on each side for a total of 30 inches x .75 = 22.5 square inches. Then 22.5 x 11 pounds per square inch = 22.5 square inches. So 22.5 square inches x 11 pounds per square inch equals 247.5 pounds total load.
So a three sided triangle made from 3/4” plywood would be able to carry 247 pounds. That is probably more than adequate for an side table.
I would note that the 11 pounds per square inch was noted as “light load”.
For my self, I would note have done the math. For my that-ought-to-be-strong-enough school of engineering, I would have just gone ahead and built it.
3/4” x 3/4” lengthwise gussets glued to the interior would greatly strengthen the joint and smaller than 10” would make installing those gussets very difficult.
More demanding would be how to attach the base to the triangle and how to attach the top to the triangle. I think I would install a triangle in the interior of the piece made from 3/4” lumber glued and attached with several pocket hole screws. The base would screw into the triangle. The pocket hole screws would be stressed in shear and they are extremely strong in that direction. I would probably used 3 screws per side (9 total) and brads to hold it in place. I would drill a 1-1/2” hole in the middle of the triangular piece so that I would have something to grab onto when adjusting the location inside the column.
My apologies. I am a fast typist, so my posts tend to be longer than most.