3D4KIDS exercise: Tiling the plane with the versatile tile

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This is part of a series of 30 exercises developed during the 3D4KIDS program, a comprehensive initiative under the Erasmus+ program that aims to enhance teachers' understanding 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 unique tiles: the "versatile" tile and another similar tile with symmetry. There are countless ways to accomplish this task. Some methods are classified as periodic, while others are considered aperiodic. This exercise employs two distinct types of tiles. Tile Number 1: Versatile All sides of this tile have equal lengths. The versatile tile can be constructed by attaching an equilateral triangle and rhombi with acute angles measuring 45, 30, and 15 degrees, as depicted above. Several examples of plane tilings are provided for illustration purposes; the first one is periodic, while the subsequent two are aperiodic. Tile Number 2: Another Symmetrical Tile This tile is derived from a regular decagon by removing a section. The angles of this tile are illustrated in the figure above.