The majority of State Capitol buildings across the country look exactly like your vision of a Capitol building: stately, with columns and a big dome that may or may not have a statue on top. In other words, a lot like the U.S. Capitol.
But a handful don’t fit into the typical neoclassical mold. Most of them are relatively new; either in younger Western states or new buildings that replaced old Capitols. Here are some of the more unique State Capitols in the country:
Built in: 1932
What it looks like: A Mormon Temple. The 400-feet-tall building is Nebraska’s third Capitol building and has 15 floors above ground. The 19-foot-tall bronze statue on top is “The Sower.”
Built in: 1932
What it looks like: The Nebraska State Capitol (except without a dome on top of the tower.) Former Gov. Huey Long (D) told architects he liked the the idea of a tower on the building, and they used the Nebraska Capitol, which was under construction at the time, as a model.

Louisiana State Capitol (“Louisiana State Capitol Building” by Chrismiceli – Own work. Licensed under Creative Commons Zero)
Built in: 1938
What it looks like: Something out of a sci-fi movie like the home of a Star Fleet commander. The 24-foot bronze and gold-leaf statue on the top is the “Oregon Pioneer.”

Oregon State Capitol (“Oregon State Capitol 1” by M.O. Stevens – Own work. Licensed under Public domain)
Built in: 1966
What it looks like: A Southwestern middle school campus (but from the sky, it looks like the Zia sun symbol, which is used on the New Mexico flag). Also known as “the Roundhouse,” it’s the only round Capitol building in the country.

New Mexico State Capitol (“New Mexico State Capitol east entrance” by N salazar – Own work. Licensed under Public domain via Wikimedia Commons)
Built in: 1899
What it actually looks like: Hogwarts. The New York Capitol is the only building on this list not built in the 20th century. It was initially designed by an Englishman who also designed the Parliment buildings in Ottawa, Canada, but two American architects eventually took over. It took 32 years to build.

New York State Capitol (“NYSCapitolPanorama” by Matt H. Wade (User:UpstateNYer). To see his entire portfolio, click here. Own work. Licensed under Creative Commons Attribution 3.0 via Wikimedia Commons)
Built in: 1969
What it actually looks like: Exactly what you’d expect the State Capitol building in Hawaii to look like, which is to say, a community college in San Bernardino or public library in Mesa, Arizona. The previous State Capitol was the Iolani Palace, the only royal palace in the U.S.

Hawaii State Capitol (“Hawaii state capitol from the south-east” by XpixuploadCamera location21° 18′ 24.34″ N, 157° 51′ 26.53″)
Built in: 1934
What it actually looks like: A high school? A high school with a prison attached, maybe? It’s the second State Capitol for North Dakota, and because it was built during the Great Depression, some of the plans, like a 50-foot statue, were scrapped.

North Dakota State Capitol (“2009-0521-ND-StateCapitol” by Bobak Ha’Eri – Own work. Licensed under Creative Commons Attribution 3.0 via Wikimedia Commons)
Built in: 1931
What it actually looks like: A county public health building. Congress approved funding for the building in 1911, but construction was delayed until 1929 for a number of reasons including a halt on all public works projects because of World War I.
Information about when buildings were built comes from dedication and completion dates from official state and local websites. h/t to everyone who responded to this tweet.