Definition
Tessellation
A tessellation covers a flat surface with tiles that leave no gaps and do not overlap.
What it means
Picture laying tiles across a tabletop. Every tiny patch of the tabletop must be under one tile: none may be left bare, and none may be covered twice. The tiles can slide, turn, or flip to fit. Their edges may meet, but their inside regions must not cross.
Remember it
Every spot exactly once: no holes and no double cover.
Example
Cover a 12 cm by 8 cm rectangle with 2 cm square tiles. Six tiles fit across and four fit down, so 24 tiles cover the whole rectangle. Their shared edges meet exactly, with no gap and no overlap, so the arrangement is a tessellation of the rectangle.
Watch for
A row of touching shapes is not enough because it does not cover a surface. Any arrangement with a hole or with one tile lying over another also fails.
Common mix-up
A repeating decoration is not automatically a tessellation; the no-gap, no-overlap covering rule is what matters.
Exact meaning
A tessellation is a covering of a flat surface by shapes called tiles, with no gaps and no overlap between the tiles’ interiors.