Hi Boni, one way to do the dome is to use a cube instead of a sphere, sounds odd but you end up with much better topology. Add a subdivision modifier to your cube with two levels of subdivision and then apply the modifier. Delete the faces so that you are left with the quarter sphere (Dome) Add a solidify modifier for thickness and apply. You are now left with a dome made of quads. Select the bottom edges and scale along the z axis to 0 to flatten the bottom of the dome. Add some controlling edge loops to tighten the edges and add another sub division modifier to smooth to the level you want.

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