Well, first, I guess I'd ask if you're planning to glue the lateral face (ie the sides of the CP) to the top or not. I'd HIGHLY recommend you do not do that! That's what I did, I regret it to this day.
Instead construct a box of the bottom and sides of the CP, then attach the top via a hinge of some sort (piano, cabinet, whatever works). That way, you can lift the top for maintenance easily.
To construct the box, cut your bottom piece as appropriate (usually it'll be the same shape as the top, but a little smaller, so that the sides are attached to the EDGE of the bottom piece, so it's edges don't show.
Then, use glue, screws, nails, whatever to attach the sides to the bottom. You can fit it all together before hand easily to test the fit and your angles.
You can also use metal or wood braces on the INSIDE to reinforce the corners, instead of just relying on glue.