Math help for UFO prop

We are trying to recreate a UFO prop and need help with the geometry. As you can see from the photo, the UFO has 16 sections, 8 large ones and 8 smaller ones. We would have a 3 foot acrylic dome in the middle. So, we would want to account for the opening. Not including the 3 foot opening for the dome, we would like each section to be 8 ft. So, the ufo would be 19 feet across, including the dome section (two eight foot sections and the 3 foot dome). We need to know the dimensions for the sections.