Carpentry and Woodworking - How to attach?

I'm building a table that has 72 triangles. The table will have 7 sides. I'm making it out of 3/4 in wood. Question: How do I attach the triangles so they hold tight for a table. I planned on several things. 1. gluing the triangles to a 3/4" plywood base but if that plywood isn't completely flat you would see it in the table top. 2. using splines and glue to attach the triangles but would that be sturdy enought. or 3. using both the above ideas togetter. Has anyone done this before and if so what do you recommend? Thanks for your help :)

I built a chess table once using walnut and ash cut into squares. I just cut them about 1/4 inch thick and glued them to a piece of plywood separating the squares with thin strips of cherry. Worked well for me but the table wasn't that big. I would use biscuits AND mount on a piece of plywood with X brace under.

What Mike said, plus, make sure the plywood is smooth, use a construction adhesive(less moisture to warp the plywood) and notched trowel. When all is dry, sand the top smooth.