In their new book, “Parliament,” the partners in XML, a creative agency in Amsterdam focusing on architecture, urbanism and research, compared 193 different legislative buildings. Despite major differences among countries and cultures, the authors were able to sort the design of parliamentary structures into five typologies: the opposing benches, derived from the medieval royal court; the neo-Classicist semicircle of 19th-century European nation-states; the horseshoe, a hybrid of the previous two; the circle (rarest of all); and the classroom (commonly found in authoritarian countries).

This relative homogeneity, the architects observe, suggests a systematic lack of innovation. The three dominant typologies (opposing benches, classroom and semicircle) were developed for the most part between 1800 and 1850, and remain mostly unchanged. The XML principal David Mulder (one of the authors, with Max Cohen de Lara, of “Parliament”), said in our recent interview:, “They are fixed in time. That’s crazy. The world has changed enormously.”

Today’s legislative buildings are responding to that change from a context that, in the case of the British Parliament, dates from 1215 when Magna Carta formalized an agreement between the king and his subordinates. The “opposing benches” typology emerged from this; early meetings took place in the nave of St. Stephen’s Chapel, creating the archetype of two long oppositional rows.

These typologies persist in an inward orientation despite the huge changes in governing, from the emergence of global convenings and agreements to the hyperlocal decision making seen at the grass roots level. Voting can be done by machine. Developments in mass media from radio to Twitter have extended and transformed the space of politics outward. Yet in the room where it happens (to steal one of Aaron Burr’s lines from “Hamilton”), the process and physical space remain frozen in time.

Could architecture help shift parliamentary politics into a new era? Mr. Mulder points out that opportunity for change may be imminent: Because so many Parliament buildings were constructed around the same time, they tend to go through similar renovation cycles. In Europe alone, the buildings in Austria, Britain, France, the Netherlands and Norway are all due for an update. Usually governments incline to preservation and restoration, but this time around a few are revealing an openness to change.