The Brussels graph is the name given on the House of Graphs website to the quintic edge-girth-regular graph 
constructed by Araujo-Pardo and Leemans (2022). It is illustrated above in a number
of bilaterally symmetric LCF embeddings.
Though not mentioned by Araujo-Pardo and Leemans (2022), the Brussels graph is isomoprhic to one of the two graphs that are cospectral
with the Wells graph (E. Weisstein, Nov. 6,
2025). In particular, as described by van Dam and Haemers (2002), it can be constructed
from the Wells graph by removing an edge 
and its antipodal edge 
(i.e., the edge whose vertices are at graph
distance 4 from the original edge vertices 
and 
) and adding new edges 
and 
.
The Brussels graph satisfies the rhombus constraints and contains no known unit-distance forbidden subgraph, yet appears not to be a unit-distance. A number of embeddings found from different initial embeddings by minimizing the sum of square deviations from unit edge lengths until a local minimum was reached are illustrated above.
