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How to Make a Tetrastix!

Figure15: Tetrastix.

Tetrastix are a non-intersecting arrangement of cylinders on the simple cubic lattice. Tetrastix arrangements can be made out of a variety of materials (post 5). Pencils will be used in this example, but any uniform rod or stick can be used. The pattern that is followed will direct the geometry and create a symmetric arrangement. Using only the compression from rubber bands and the friction of the rods, this arrangement can be used to make a beautiful and complex mathematical model.  

Materials: 18 uniform sticks, 6 rubber bands, glue (optional). 

time: >20 minutes 

Figure16: Tetrastix materials.

To start, 6 sticks are brought together and bound on both ends with rubber bands to make a small bundle, step 1 figure17.


Next, we take 3 new sticks and insert them at a right angle, between 2 and 4 sticks of the 1st bundle, then 3 additional sticks are inserted into the 1st bundle so the spacing of the 2 crossing groups is 2-3-2-3-2. The 6 new sticks are then bound with rubber bands on each end, step 3 figure17.

Now, just one stick at a time is inserted perpendicular to the 2 bundles, pushing apart and poking through the crossing rows. Then, another rod is inserted between the rows of 2 rods, that also pushes apart 2 rods along the rows of 3. The final 4 rods are placed outside of the rows of 2, and inside the rows of 3, and the 6 new rods are bound together (step 6 figure17). Last, the elastics are tightened and spaced evenly in order to complete the symmetric arrangement (figure18). The rubber bands can be removed only if the tetrastix is glued together (figure 15).

Figure17: Tetrastix Steps 1-6.

Congratulations! You now know how to make a simple tetrastix model! These basic principles can be extended and used to make even more complicated structures and an infinite array of novel designs.

Figure18: Tetrastix  18 Pencils.

More tertastix patterns and modeling examples coming in the next blog posts. 

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 copyright 2021 Anduriel Widmark