Given that the current ultraviolet (UV) networking model is established in a regular circular area, this article studies the coverage of a UV non-line-of-sight (NLOS) communication network creatively in the arbitrary polygon area. In this paper, the UV communication model and the basic concepts of network coverage are introduced first. Then the influence parameters of the UV node communication radius are studied, and the changes of the communication radius under different work patterns are analyzed. Finally, the coverage of the square target area is simulated under different communication parameters (transmitted power, data rate and node density). The results illustrate that the smaller the transceiver elevation angles are, the better the network coverage performance is. Additionally, we numerically compare the UV network models of polygonal and circular regions, which can be used as a reference for actual networking.