It is known as The Roundhouse. It was dedicated on December 8th, 1966, which happens to be just a couple weeks after my birth. I am not saying that my arrival had anything to do with it, but you never know.
The roundhouse was designed in the shape of a Zia, the symbol of NM.
Around the building itself there is 6.5 acres of land with gardens containing over 100 varieties of plants along with numerous statues of the native pueblo people.
The style was finally considered right and proper for New Mexico.
Although personally I prefer the look of that looming Victorian building that was burnt to the ground, I do have to admit that this building fits better for Santa Fe and all of New Mexico. It is far more representative of the cultures and style here, which is really what a state capital building should reflect.