The Assembly is the most sculptural and eye catching of all the geometrical forms of the Capitol. Le Corbusier designed a great hyperbolic drum, 39 mt in both diameter and height was incorporated in the plan along with a pyramidal skylight connected to the drum by a small bridge. The building has two entrances, one at the basement level for everyday use and the other from the piazza level for ceremonial occasions through a massive entrance, 7.60 mt high and 7.60 mt broad, whose enameled door (a gift to Punjab from France) translates a cubist mural painted by Le Corbusier himself.  The door and many other elements of the Capitol demonstrate Le Corbusier's predilection for melding art and architecture.

The large cuboid base of the hyperbolic drum contains the independent volumes of the upper and the lower chambers, now divided between the Punjab and Haryana states as their respective legislative chambers. The outer box acts like a container of two auditorium-like spaces used by the two Legislative Assemblies. An irregular space between the two chambers is a large lobby with sculptural lights designed by Le Corbusier. This area is animated by the discussions of legislators during breaks in the Assembly sessions.