Because the simplest example of the series is not particularly pleasing I chose to present the most complex first. There are five members of the series with 32, 16, 8, 4, and 2 planes of symmetry each. all planes are vertical and all intersect at equal angles at the center of the plan view of the dome. At the end I have included an additional example of 2 planes of symmetry which is more complex.
All the diagrams represent the central dome on top of the prior YouTube animation. The two colors indicate the way the central dome is expanded on the successive tiers. The final example of necessity uses six colors as a guide to its expansion.