The Danzer graph is the Levi graph of the Danzer configuration (Boben et al. 2015). It has 70 vertices and 140 edges and is quartic, bipartite, self-dual, and unit-distance. It is illustrated above in a unit-distance embedding (left) an LCF embedding of order 5 (center; Boben et al. 2015), and a bilaterally symmetric LCF order-1 embedding (right; E. Pegg Jr., pers. comm., Oct. 30, 2022).
The Danzer graph is isomorphic to the middle layer graph of order 3 and the bipartite Kneser graph . It is the bipartite double graph of the odd graph .
The Danzer graph is distance-regular (Brouwer and Koolen 1999) and distance-transitive.
The Danzer graph is implemented in the Wolfram Language as GraphData["DanzerGraph"].