A simple (non overlapping) region of the hexagonal tessellation of the plane is uniquely determined by its boundary. This seems also to be true for "regions" that curve around and have a simple overlap. However, Guo, Hansen and Zheng  constructed a pair of non isomorphic (self-overlapping) regions of the hexagonal tessellation which have the same boundary. These regions overlapped themselvas several times. In this paper we prove that any region not uniquely determined by its boundary must cover some point three or more times.
|Original language||English (US)|
|Number of pages||8|
|State||Published - Nov 5 2003|
ASJC Scopus subject areas
- Computer Science Applications
- Computational Theory and Mathematics
- Applied Mathematics