What Is a Tiling?
What is a Tessellation? || Tessellation Tutorials || Tessellation Links
When you fit individual tiles together with no gaps or overlaps to fill a flat space like a ceiling, wall, or floor, you have a tiling. You can imagine that you can use a variety of shapes to do this.
Here are some examples:
Another word for a tiling is a tessellation. Read more here: What is a Tessellation?
A special kind of tiling or tessellation is rep-tiling. No, these rep-tiles aren't living things, although some of you might be thinking of the figures in some of M.C. Escher's work. The "rep" in "rep-tile" stands for "replicating." Rep-tiles can be joined together to make larger replicas of themselves.
Another special kind of tiling or tessellation is Penrose tiling named after the British physicist and mathematician, Roger Penrose. The tiling is comprised of two rhombi, one with angles of 36 and 144 degrees and one with angles of 72 and 108 degrees.
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