The structure is based on two components:
Its important to note that these two dissimilar halves must meet and be attached. There is likely to be some mismatch between the two so one will have to be flexible enough in design to allow for small adjustments. The wooden base seems likely since the math will be easier.
The conduit dome will be made of 1/2 or 3/4 in conduit which is thinner than the 2"x4" lumber used for the walls. The 2"x4" lumber walls will have an appreciable inner vs outer radius (a difference of 4" actually :) ). Its preferable for the metal dome to rest along the middle to outside of the wooden base. This is because there will be about 3 or 4 inches of lighting and covering on the inside of the dome. It would be ideal if this extra thickness met the inside of the wooden base rather than extending past it into the space.