I've been having some fun lately making drawings of some famous configurations of points and lines (in most cases with equal numbers of points per line and equal numbers of lines per point). You can go read the Wikipedia article if you want detailed explanations, but here are just the pictures.

The Cremona–Richmond configuration, whose points correspond to pairs of elements from a six-element set and whose lines correspond to triples of disjoint pairs:

Cremona–Richmond configuration

The Hesse configuration, formed from the inflection points of an elliptic curve in the complex projective plane but impossible to realize in the Euclidean plane:

Hesse configuration

The Reye configuration of the edges and long diagonals of a cube:

Reye configuration

The Perles configuration, not as uniform as the other ones but with the golden ratio hiding inside it, forcing it to have irrational vertex coordinates:

Perles configuration

And here are two older drawings with new articles. The Schläfli double six:

Schläfli double six

And the Desargues configuration:

Desargues configuration