The frame requires only one special angle throughout, 17 degrees from vertical. This is the angle I set my hand held circular saw for all the cuts. Look carefully at how the corners go together, carefully determine lengths of pieces from the dimensions. For instance, the top and bottom pieces show a measurement of 24" corner to corner, but that is the short dimension. The angles widen from there. This is a real measure twice cut once situation. I found it helpful to lay out the hexagon on a sheet of plywood, and assemble the pieces on there. Then the frame will not get distorted during assembly.
This hexagon can be drawn most easily and accurately by first drawing a tall rectangle 24" wide and 78" tall. A horizontal bisector (cuts it in half) extending 12" out on each side will reach the remaining corners. The door is of course smaller than the frame by the width of the frame all around (so it will fit inside) plus another 1/8" so it won't stick tight.
I fastened my frame together with metal plates made from leftover sheet metal (9" squares will do), and 1" #10 sheet metal screws. The plates are bent around the six outside corners of the frame. I fastened the frame to the plywood with 10 short blocks of 2x4 around the inside, lagscrewed through the plywood into the blocks, and nailed through the frame into the blocks. During this step I had the frame braced with diagonal pieces of wood to keep it from distorting. A stop running around the inside of the frame of 1x4 pine covers some of the nails and holds the door in place when shut. The door itself is fastened together with many 1 1/4" #10 sheet metal screws, through the plywood into the wooden braces. If you use 1" wood inside the door, use 1" long screws.
The virtue of this hexagonal door is that the door does not need to be lifted much when it swings inward, because it does not rise much, and does not have much momentum when it is closed, outward. The angle where the hinges mount on the door counters the outward tilt of the door and minimizes the unwieldy quality of other designs I have tried. I welcome innovators to try round doors. The hinges on round doors require special attention. A round door with a small, vertical flat side to mount the hinges would help the situation. Doors get a lot of use. We are a much happier family now that we have a door that functions properly. A poorly performing door is a constant annoyance.
I have included a drawing which shows how to locate the corners of the hexagon from the inside of the assembled dome. The corners of the triangular vertex holes, and the bottom center of a base sheet of plywood, are the reference points. Assume right angles where it appears to be so. Drill the six corners through to the outside, and connect them with straight lines, and saw the hole when you are satisfied it is a close fit to the frame. The frame, when properly braced to hold it rigid, can be held up to the inside of the dome, corners matched with marks or holes, to anticipate the fit.
Once the frame is in ,and the door hung, the frame should be flashed or caulked to seal it tight to the dome. A stop running around the inside of the frame of 1x4 pine or some appropriate trim covers some of the nails and holds the door in place when shut.