The Kummer graph is the name apparently first adopted here for the Levi graph of the 
Kummer configuration (Coxeter 1950), corresponding
to the folded 6-cube graph (Brouwer et al.
1989, p. 264). It is isomorphic to the graph formed from the 6-hypercube
graph where vertices opposite to one other (i.e., at maximal graph
distances from each other) are vertex-contracted
together. It is illustrated above in several order-2 LCF
notation embeddings.
It is implemented in the Wolfram Language as GraphData["KummerGraph"].
The Kummer graph has graph genus 9 (E. Weisstein, Jan. 13, 2026).
