I'm just starting to study tilings in a groups and geometry module, and I'd like some confirmation of my understanding of precisely what it is which differentiates a single tile, from a tiling- when it is considered as part of a tiling. Perhaps I misunderstand, but it seems that a tiling can be considered as an arbitrarily large assemblage of tiles, and also as a single tile, whose vertices and edges are determined by the other tiles that it is in contact with?
I figured it would be best to illustrate my interpretation. So I will re-edit later, with images!
Hexagonal tiling. This is a tile (or polygon), with 6 vertices, and 6 edges. This relationship is the same regardless of whether the tile is thought of in the context of a tiling or a polygon
Brick tiling. Each tile, in this case, when considered as part of a tiling, has 6 vertices, and 6 edges.
However, it doesn't seem completely clear what exactly the distinction between a tile and a tiling is? A tiling could presumably be an arbitrarily large collection of tiles, or just one?
(I'm observing the tiling in terms of the tiles which are adjacent to a single tile)
