This is a tile that can be used to form both periodic as well as 'aperiodic' tiling patterns. One of the aperiodic patterns formed using this tile shape is called the 'Voderberg' tiling pattern (eg. http://www.insite.com.br/art/fractal/voderberg/berg.htm).
This is an example of a SINGLE tile shape being able to achieve aperiodicity. https://www.shapeways.com/model/2935431/sphinx-aperiodic-tile.html?li=shop-results&materialId=6