## 1 Introduction
This algorithm performs well and has good spatial expansibility, which can be expanded to a 3D scenario. The unmanned aerial vehicle (UAV) industry has been growing at a tremendous speed in the recent years. Sensor nodes can be carried on the UAVs to inaccessible locations and be used in a lot of real applications, such as desert, deep sea, or deep space, which can substantially expand people's ability to detect information. All those applications may require a 3D node deployment for a relatively large-scale sensor network [21]. Based on the UAV's high mobility, [PERSON] et al. [22] designed an equal service distance algorithm to maintain a superior surveillance performance. [PERSON] et al. [23] proposed a system inspired from the biological cell differentiation through hormones that can coordinate the sensing effort to form a distributed sensor network for UAVs. [PERSON] [24] introduced a distributed coverage control laws to guarantee optimal sensor self-deployment over three-dimensional sensing fields. However, the UAV-assisted 3D WSN still lacks good node deployment algorithms for its further applications. It is well known that the optimal structure of a sensor network in a two-dimensional plane is a regular hexagonal network structure, but the optimal coverage model in three -dimensional space is still controversial. [PERSON] and [PERSON] already demonstrated that the node utilization of the body-centered cube structure (BCCS) is up to 68.3%, which indicates that the spherical coverage model of the body-centered cube structure may become the most economical one in the three-dimensional space [25]. The Voronoi units of all nodes in the spherical coverage model of the body-centered cube are the truncated octahedrons, which can also be infinitely stitched into a larger three-dimensional space and form the most thermodynamically stable crystal. [PERSON] et al. have truncated the octahedron vertices to locate sensor nodes to achieve a 3D WSN with the fewest nodes [26]. This deployment algorithm will obtain seamless sampling coverage and high connectivity at the same time. [PERSON] et al. filled a 3D space with a truncated octahedron for target-range coverage to improve the performance limitations in underwater communications via sound waves [27]. Experimental results by [PERSON] et al. [28] and [PERSON] et al. [29] suggest that, for a seamless 3D structure with minimal number of nodes, a truncated octahedron is the best choice for filling the defined space. Therefore, the spherical model with truncated octahedrons as structure units in space is a good 3D coverage model. In this paper, for the first time, we present a three dimensional network deployment algorithm inspired by physical dusty plasma crystallization theory in large-scale WSN applications. The 3D node deployment algorithm (VFA-DP-3D) and corresponding equations developed from the dusty plasma theory are presented. We also introduced four kinds of evaluation methods in 3D space, such as the moving distance, the spatial distribution diversion, the system coverage rate and the system utilization. We used different ways to analyze the final performance of our 3D WSN deployment based on these four conditions. These evaluation methods can importantly present the validation of the 3D WSN deployment. It can be clearly seen from all experiments that our VFA-DP-3D algorithm can successfully achieve a better spherical stack of truncated octahedrons in a 3D space, which may have a maximum coverage rate of 0.8. Furthermore, the parameter effects of the Debye length and the node sensing radius have also been discussed. We innovatively combined the system coverage rate and the system utilization to find an optimal sensor radius and improve the final deployment network if the sensor network has the largest perception range and relatively small system redundancy.