Establish Rao’s classification of convex pentagonal monotiles

Establish whether all convex pentagonal monotiles belong to the 15 known Type families, thereby determining whether Rao’s classification claim is correct and whether every convex pentagonal monotile can generate a periodic tiling.

Background

The paper summarizes the 15 known families of convex pentagonal monotiles and notes that Rao claimed these families exhaust all convex pentagonal monotiles. If this classification is correct, every convex pentagonal monotile belongs to one of the listed families, each of which admits a periodic representative tiling. The paper therefore identifies definitive verification of Rao’s claim as unresolved.