Average distance between nearest neighbors for randomly placed points in a unit square?

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The answers I found were generally about the distance between any two points in a square. I'm trying to find the average distance between nearest neighbors.

Background on this is I'm processing 3D point cloud data. Generally the points define a surface in 3D space, and the linear spacing between the points is important to me. I can easily find there are, say, about 30 points per square inch, and what I'm trying to calculate is the average distance between nearest neighbors. I could do this empirically but wanted to understand it better.

I found this: How to compute the expected distance to a nearest neighbor in an array of random vectors? But unsure how to interpret this for points.