The Grünbaum-Rigby graph is the term used in this work for the Levi graph of the Grünbaum-Rigby configuration. This graph has 42 vertices and 84 edges. It is illustrated above in a number of embeddings.
The graph is regular and Hamiltonian and is illustrated above in a number of LCF embeddings.
The Grünbaum-Rigby graph has automorphism group order 672. By comparison, the Levi graph of the Berman-Gévay-Pisanski configuration has automorphism group order 12, so the two graphs are nonisomorphic (Berman et al. 2024).
The Grünbaum-Rigby graph has graph genus 8 (E. Weisstein, Jan. 13, 2026).
It is implemented in the Wolfram Language as GraphData["GruenbaumRigbyGraph"].
)
Polycyclic Configuration." Electron. J. Combin. 31, #P4.54, 2024.
)." J. London Math. Soc. 41, 336-346,
1990.