Configuration

Summary

A configuration is a finite system of points and lines in which two points share at most one line. Every point lies on the same number of lines, and every line contains the same number of points. A configuration with $p$ points on $\gamma$ lines each and $\ell$ lines with $\pi$ points each is written $(p_\gamma\ \ell_\pi)$, and $(p_k)$ when $p = \ell$ and $\gamma = \pi = k$. Many classical theorems of projective geometry, such as those of Desargues and Pappus, are statements that certain configurations close up.