Three Regular Tessellations

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Theorem

There exist exactly $3$ regular tessellations of the plane.


Triangles

Equilateral triangles form a regular tessellation:


RegularTriangleTessellation.png


Squares

Squares form a regular tessellation:


RegularSquareTessellation.png


Hexagons

Regular hexagons form a regular tessellation:


RegularHexagonTessellation.png


Proof


Sources