The 13th Immortal by Robert Silverberg

The ducal capital of Chicago sprawled in a lazy ring on the banks of Lake Michigan, in Illinois Province. As Dale Kesley and his small retinue waited outside the city's walls before requesting admission, the thought occurred to him once again that the world's cities were similar. As he looked at Chicago, it seemed to him that he might never really have left Buenos Aires.

Duke Winslow's palace, visible high in the background overlooking the calm lake, might have been an exact replica of Don Miguel's, except that its flat walls were hewn from broad slabs of flesh-red feldspar instead of spun, as Miguel's were, from shimmering polyethylene. In the stagnant, late-August air, the sun's rays hit the palace walls weakly, giving them an oily glare that Kesley found displeasing. But still he preferred the natural blockiness of the stone to the consistent slickness of the plastic that formed the walls of Miguel's palace. Polyethylene walls were the products of controlled hard radiation and, controlled or no, Kesley, like all men, found the concept of radiation repugnant. It jarred against ingrained taboos.