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How can I build a dome on top of a building, similar to a state capital or something similar?

The building has a base of 16x24 studs.

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up vote 8 down vote accepted

As a dome is typically a hemisphere, this topic about building spheres might be very useful for you. There's also an automatic tool to construct spheres that you could use to get an ldraw-plan.

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Like oezi said you can build a dome out of cascading bricks, which is perfect for most scales of building. For smaller scale building where you'd want a less jagged approach you may want to use a combination of 1/4 dome pieces. A complete dome will take up an area of 6x6 studs wide.

This technique is common in the Prince of Persia sets.

The Fight for the Dagger

For a true miniland scale building you may want to have a closer look at the model in Legoland Florida.

enter image description here

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