3D4KIDS exercise: Tiling the plane with the versatile tile

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This is one of thirty exercises developed during the 3D4KIDS program, designed to enhance teachers' knowledge of 3D printing technology through targeted training materials. For more information about this Erasmus+ initiative, visit https://www.3d4kids.eu. The activity involves tiling a plane with two types of tiles: the 'versatile' and its similar counterparts. An infinite number of ways exist to achieve this, categorized as either periodic or aperiodic tilings. The exercise utilizes two distinct tile designs. Tile Number 1: Versatile Each side of this tile is identical in length. It can be constructed by combining an equilateral triangle with rhombi featuring acute angles of 45, 30, and 15 degrees, as depicted above. Multiple plane tilings are showcased for reference, including a periodic example followed by two aperiodic examples. Tile Number 2: Symmetric Tile This tile is derived from a regular decagon by removing a segment. The figure above illustrates the angles of this tile. Two tilings are displayed below – one periodic and the other aperiodic.