Reptiles with Holes
Proceedings of the Edinburgh Mathematical Society
Croft, Falconer and Guy asked: what is the smallest integer n such that an n-reptile in the plane has a hole? Motivated by this question, we describe a geometric method of constructing reptiles in Rd, especially reptiles with holes. In particular, we construct, for each even integer n ≥ 4, an n-reptile in R2 with holes. We also answer some questions concerning the topological properties of a reptile whose interior consists of inﬁnitely many components.
Jordan, Francis, Sze-Man Ngai.
"Reptiles with Holes."
Proceedings of the Edinburgh Mathematical Society, 48 (3): 651-671.
doi: 10.1017/S001309150400001X source: https://www.cambridge.org/core/journals/proceedings-of-the-edinburgh-mathematical-society/article/reptiles-with-holes/7B77AE5C796E5FD04E67F2107967C9FD