An incomplete Voronoi tessellation

This paper presents distributional properties of a random cell structure which results from a growth process. It starts at the points of a Poisson point process. The growth is spherical with identical speed for all points; it stops whenever the boundaries of different cells have contact. The whole process finally stops after time t. So the space is not completely filled with cells, and the cells have both planar and spherical boundaries. Expressions are given for contact distribution functions, the specific boundary length, the specific surface area, and the mean chord length of this cell structure in ${\displaystyle {ℝ}^2}$ and ${\displaystyle {ℝ}^3}$.