The Hessian configuration is a (94,123) with 9 points, 3 on a line, and 12 lines, 4 through each point. A model of this configuration can be found in the Hessian polyhedron 3{3}3{3}3. The POINTs are the nine diameters of the polyhedron:
and the rotated versions of these three. The LINEs are the polygons 3{4}2:
and rotated versions of these four.
To verify that the configuration is a (94,123), observe that the first POINT is incident with the first three LINEs and with this fourth:
It is easy to see that each LINE has 3 triangular POINTs.
see also the Wikipedia page:
Frans Marcelis 