The original monotile paper https://arxiv.org/abs/2303.10798 https://arxiv.org/abs/2303.10798 mentions that (at the time that was written) the minimum number of

The original monotile paper https://arxiv.org/abs/2303.10798 https://arxiv.org/abs/2303.10798 mentions that (at the time that was written) the minimum number of sides had to be 5 <= n <= 13, but also that a smaller tile can't be a polykite like the hat; exhaustive search had shown that there were no other aperiodic monotiles (than the hat and turtle) with < 21 kites But a correction: the basic shape of the spectre is 14 sides with 2 of them colinear. It's only truly aperiodic when you modify the 14 edges, making it clear it is 'really' 14 sided not 13.