Superiority of network coding in space for irregular polygons

Network coding in space elicits a new research direction lying at the intersection of information theory, networking and geometry. And it's meaningful to unearth the potential superiority of network coding in space. In this paper, the constructions of network coding in space and routing in space are implemented for irregular polygons with a concave node, which haven't been covered in literatures yet. And quantitative computation of a range for network coding outperforming routing under irregular polygons is given by mathematical calculation and Matlab. Several properties of network coding in space are found by induction and they lays a foundation for the problem of an arbitrary point set in space. Moreover, analysis of the comparison between network coding in space and routing in space are presented, and concluding remarks are given finally.