Tiling the plane with the versatile tile

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This exercise is part of a series of 30 activities developed during the 3D4KIDS program, an Erasmus+ initiative that aims to enhance teachers' knowledge of 3D printing technology by creating specialized training materials. For more information, visit https://www.3d4kids.eu. The activity involves tiling a plane with two types of tiles: the versatile tile and other similar tiles. There are infinitely many ways to achieve this, including periodic and aperiodic tilings. Two kinds of tiles are used in this exercise. Tile number 1: The Versatile Tile All sides of this tile are identical in length. It can be constructed by attaching an equilateral triangle and rhombi with acute angles measuring 45, 30, and 15 degrees, as shown above. Several examples of plane tilings are provided, including one periodic and two aperiodic arrangements. Tile number 2: Another Symmetric Tile This tile is similar to the versatile tile but is symmetric in design. It can be obtained by removing part of a regular decagon. The angles of this tile are clearly shown in the figure above.