Smallest bipartite graph forced by planar two-colorings

Determine the smallest-order bipartite graph $H$ for which every 2-coloring of the Euclidean plane contains a monochromatic unit-copy of $H$.

Background

The paper proves that the 11-dimensional hypercube Q_{11} has planar Ramsey number 2, but asks for the smallest bipartite graph with this property.

References

What is the smallest order of a bipartite graph $H$ such that $#2{^2}{H}=2$?

— Ramsey problems for graphs in Euclidean spaces and Cartesian powers (2512.15516 - Axenovich et al., 17 Dec 2025) in Question Q_bipartite, Section 6.1 (Planar case)