The author built the cupola base out of two layers of 3/4-inch exterior plywood. Two long strips of thin plywood act as a giant bevel square to transfer the angle of the roof to the base.
To give the base a paneled look, the author attaches 1x stock around the perimeter of each side.
After setting the base at its location on the roof, author beds attachment blocks in silicone and screws them into the roof.
A bead of silicone seals the slanted edges of the base to the roof, but the lower horizontal edges of the base were left clear to allow moisture to drain away.
After receiving three coats of exterior paint, the louvered section screws to the base at each corner.
The swooped roof section tops off the assembly. Note, before the roof was permanently attached, insect screening was stapled to the inside of the louvered section.
Long screws extend from the frame up into the rafters to secure the roof in place.