Refined rectangle covering bound for the icosidodecahedron

Compute the refined rectangle covering bound of the icosidodecahedron’s slack matrix and determine whether it closes the gap to the known upper bound of 12 for its non-negative rank.

Background

The paper computes an RCB of 11 for the icosidodecahedron, improving its lower bound on non-negative rank. However, the RRCB is not computed, and the current bounds leave a gap between 11 and the upper bound 12. Establishing the RRCB could potentially close this gap if it reaches 12.

References

We were not able to compute the RRCB of the icosidodecahedron. We assume this would close the gap to the upper bound of 12 of the $r_+$.

— Computing Lower Bounds on the Non-negative Rank via SAT Solvers  (2610.11950 - Engel et al., 8 Oct 2026) in Section 4, subsection “RRCB”; Section 5, subsection “Known Values of Lower Bounds and the Non-negative Rank”