5-14-2022

How to Make a Hexastix!

Figure 59: Hexastix 28 pencils.

Hexastix is a symmetric arrangements of non-intersecting prisms that lie on the body-centered cubic lattice. Hexastix can be modeled with a variety of materials (post 5), pencils will be used in this example, but any uniform rod or stick can be used. The pattern followed will direct the overall symmetric construction in a hexastix. Only the compression from rubber bands and the friction of the sticks will be used to make a beautiful and complex mathematical model of hexastix.

Figure 60: Hexastix 28 pencils.

Materials: 28 uniform sticks, 8 rubber bands, glue (optional).

Time: >20 minutes.

To start, 7 sticks are brought together and bound on both ends with rubber bands to make a small bundle, Step 1: figure 61.

Step 2: Next, 7 new sticks are inserted at a right angle between 2 and 3 sticks of the 1^{st} bundle, so the alternating spacing of the 2 crossing groups is 2-2-3-3-2-2. The 7 new sticks are then bound with rubber bands on each end.

Step 3: Now, just one stick at a time is inserted perpendicular to the 2 bundles, pushing through the crossing rows, between 2 and 5 sticks in each bundle of 7.

Step 4: A new stick is then inserted with a similar spacing to the 1^{st }bundle as the last step, but pushing between 3 and 2 sticks from the group of 5 sticks in the 2^{nd} bundle.

Step 5: Another new stick is then inserted in a similar spacing to the 1^{st} stick, in relation to the 2^{nd} row, but now pushes between 3 and 2 of the 5 sticks of the 1^{st} bundle.

Step 6: A 4^{th} new stick is then inserted between 2 and 3 sticks of each bundle, making a square pattern.

Step 7: A 5^{th} new stick is then added between 2 and 5 of the 1^{st }bundle and outside the 2^{nd} bundle.

Step 8: The 6 and 7^{th} sticks are added outside the 1^{st} bundle, with one inside the 2^{nd} bundle, and the ends of the new 7 rods are bound on each end with rubber bands. This is now a tetrastix made with 21 sticks, consisting of a distorted hexagonal pattern on each axis.

Step 9: Next, the bundle of sticks is placed with the erasers from each axis facing down, touching the ground (this will ensure proper tetrahedral symmetry, when using directional sticks/pencils). Then, the holes running though the structure should be identified by looking directly down from above (looking through a 3-fold axis)

Steps 10-15: The entire structure is then compressed slightly by pressing down on each axis, and 7 new sticks are inserted facing down (skewered) though the 3 bundles to create a 4^{th} axis with a hexagonal pattern. The 7 new sticks are then bound together on each end with rubber bands.

Last, the elastics are tightened and spaced evenly to complete the symmetric arrangement (figure 60). Rubber bands can be removed only if the hexastix is glued together (figure 59 and 62).

Figure 61: Hexastix steps 1-15.

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

Figure 62: Hexastix 28 pencils.

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

copyright 2022 Anduriel Widmark