Planarity conjecture for golden tilings with nondegenerate weak alternation

A golden tiling is a tiling by the rhombohedra associated with the icosahedral construction, and nondegenerate weak alternation means weak alternation with no infinite run of rhombohedra all of the same type. Planarity conjecture. A golden tiling with nondegenerate weak alternation is planar. The preceding discussion notes that weak alternation alone does not force planarity, while this nondegenerate version is proposed to restore it; the status of the conjecture is not established in the supplied text.