Projective Geometry’s graphs:
OEAGOT Fano Incidence Graph | alias Heawood graph and 6-cage.
OEAGOT Pappus Incidence Graph |
External link to Coxeter’s classical 1950 article https://projecteuclid.org/journals/bulletin-of-the-american-mathematical-society/volume-56/issue-5/Self-dual-configurations-and-regular-graphs/bams/1183514923.pdf . This includes a more advanced account of the above incidence graphs, as well as various of their close relations.
Other graphs from basic Flat Geometry:
Line and Circle Theorems from Euclid to Euler: Underlying Graphs Geometrical Graphs |
institute-theory-stem.org 