Tessellation is normally emplyed to create 2D patterns and its applications can easily be seen if we care to look around for it: pavement design, textile design, math class... The list goes on. Out of many tessellations hexagonal & triangular based tessellations show unusual characterisics.
There is a strong relationship between these polygons and our eyes to interpret them as rectilinear entities. This simple fact makes it possible to create many complex rectilinear structures. However, this method creates only one type of true 3D tessellation, aka honeycomb.
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The following instruction shows how it is done.
A triangle is drawn and lines are drawn in as above. The configuration of these lines inside the triangle determines how the final structure will look. Oncce completed the triangle and its contents is mirrored aroung A-B axis, resulting in the following shape.
The next step is to array the whole lot around vertex B, which produce the following shape.
Now a rectilinear structure has emerged as a result. Since the structure is enclosed inside a hexagon and hexagons tessellate to form 2D honeycomb tessellation, it is only natural to do the same for the hexagonal shape above.
As hexagon tessellates, the structure inside it tessellates as well creating a pattern above. Some lines are confusing to the eye and ,therefore, removed to reveal the following structure.
The structure is then colored in accordance with the angle of the light source. The shaded part in the pattern above reveals a module that fits with others.
The image above can be down loaded and color them yourself to see how the final structure look! More rectilinear structures can be found at the following structure page.