The first thing the Lights do when starting a correction is to build towers surrounded by six pillars all over the planet. The towers act as a storage facility for their technology, while the pillars act as transmitters for everything from communications devices to fields created by the towers. Unlike the waypoints the towers are constructed from normal matter. Before the current correction the Lights had never needed more than one hundred towers, so felt no reason to build time moveable structures from short matter.
Towers are always built with six pillars. Most of what the Lights do is based around the number six, mainly because they each have six primary mind tendrils. The first towers that were create, billions of years ago, had a sole purpose of letting the Lights communicate over great distances. A Light would connect its mind to the central tower, then use the computer within to communicate. Each pillar acted as a placeholder for their mind tendrils which had been connected to the computer. Over the eons the towers inner working advanced, allowing a connection with a single mind tendril. But hte original design of one tower with six pillars was never lost.
Before intelligent organic life appeared in the universe, the only structures the Lights built were tower and pillars. They had no need for shelter, and any research they did happened inside the towers computer system, with practical experiment happening in the open universe. Almost all the other structures they built were for other life forms. There are some exceptions though: Core, the Lights artificial multi mind, and a small number of Lights who consider themselves to be artists or philosophers chose to experiment with building structure which had no purpose but were esthetically pleasing to them.