Rep-Tiles

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A 2D shape that can tile itself with
n
smaller, equally sized copies of itself is called a rep-tile and is said to be rep-
n
.
The order of a rep-tile is the smallest number
n
such that the tile is rep-
n
.
Any polysquare that tiles a square is obviously a rep-tile. These trivial cases are omitted here.

Details

A shape that tiles itself using different sizes is called an irregular rep-tile (or irreptile). Irreptiles are investigated in a separate Demonstration.

References

[1] M. Gardner, "Rep-Tiles," The Colossal Book of Mathematics: Classic Puzzles, Paradoxes, and Problems, New York: W. W. Norton & Company, Inc., 2001 pp. 46–58.

External Links

Rep-Tile (Wolfram MathWorld)
Irreptiles Database
Irregular Tilings
Regular Tilings
3D Rep-Tiles and Irreptiles
Perfect Tilings

Permanent Citation

Karl Scherer, George Freeman, Erich Friedman
​
​"Rep-Tiles"​
​http://demonstrations.wolfram.com/RepTiles/​
​Wolfram Demonstrations Project​
​Published: January 26, 2016