Multi-tile decoration of higher-order j skeletons

Investigate whether metallic-mean L-system skeletons with symmetry parameter j greater than 4 can be decorated using more than one type of polygonal tile to produce valid plane tilings.

Background

The authors show that for j > 3, two-tile decoration schemes (using rhombuses and regular polygons with internal angle 2π/j) face geometric inconsistencies that prevent reproducing closed-curve forms of connected thin rhombuses, particularly evident at j = 5.

They explicitly pose the open question of whether more sophisticated, multi-tile decoration strategies could successfully decorate these higher-order skeletons to achieve plane tilings.