Completeness of Rao’s 15-family classification

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

Background

The paper relies on Rao’s assertion that the known 15 Type families exhaust all convex pentagonal monotiles. If this assertion is correct, the representative tilings associated with those families show that every convex pentagonal monotile can generate a periodic tiling. The paper explicitly records that the assertion has not been conclusively verified.