Any Quadrilateral Can Tile

Initializing live version
Download to Desktop

Requires a Wolfram Notebook System

Interact on desktop, mobile and cloud with the free Wolfram Player or other Wolfram Language products.

Any quadrilateral tiles the plane. The tiling is formed by rotating by 180° about the midpoints of its sides. The same process is then applied to the four new quadrilaterals, and so on.


Another approach is to use the parallelogram formed by joining the midpoints of 's adjacent sides. Tile the plane with in the obvious way. Translate the parts of from the copies of adjacent to across into the opposite copy of . Then copy the three different patterns in the copies of to form the same tiling as before.

The tiling works whether is convex or not, simple or not, and even when is 3D.


Contributed by: George Beck (March 2011)
Open content licensed under CC BY-NC-SA



Feedback (field required)
Email (field required) Name
Occupation Organization
Note: Your message & contact information may be shared with the author of any specific Demonstration for which you give feedback.