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We consider the structure of the plane-line incidence matrix of theprojective space $\mathrm{PG}(3,q)$ with respect to the orbits of planes andlines under the stabilizer group of the twisted cubic. Structures ofsubmatrices with incidences between a union of line orbits and an orbit ofplanes are investigated. For the unions consisting of two or three line orbits,the original submatrices are split into new ones, in which the incidences arealso considered. For each submatrix (apart from the ones corresponding to aspecial type of lines), the numbers of lines in every plane and planes throughevery line are obtained. This corresponds to the numbers of ones in columns androws of the submatrices.

Twisted cubic and plane-line incidence matrix in $\mathrm{PG}(3,q)$