3D Tessellations
 
 

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A tessellation or tiling of the plane is a collection of plane figures that fills the plane with no overlaps and no gaps. One may also speak of tessellations of parts of the plane or of other surfaces. Generalizations to higher dimensions are also possible. The tessellation is perhaps most well-known today for its use in the art of M.C. Escher.

In Latin, tessella was a small cubical piece of clay, stone or glass used to make mosaics. The word "tessella" means "small square" (from "tessera", square, which in its turn is from the Greek word for "four"). It corresponds with the everyday term tiling which refers to applications of tessellation, often made of glazed clay.                --------Wikipedia-------

Tessellations don't have to be confined to 2D (surface). The concept can be extended to 3D space. One of the best example of 3D tessellation is a cube they can be stacked up or sideways. Likewise the example below can, in fact, be stacked up and sideways. However, there is one trick. The one level (or layer) up requires mirror image of the block tiles used in the previous level. Therefore, this can't  truly be called 3D tessellations

 

Paul Bourke has kindly reworked the above images to produce the following images using POV-Ray.

 

This image is the perspective version of the above tiling.

 

Another perspective view from a different angle.



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