All Models and representations of hexastix are finite subsets of an infinite hexastix arrangement. The geometry of hexstix models can be efficiently designed in 2-dimensions, as each axis has a repeating pattern that lays on the body-centered cubic lattice.
Figure 80: Hexastix grid.
Figure 81: Hexastix grid.
To start designing hexastix, patterns can be drawn on a grid (figure 68) composed of a hexagonal pattern that lays atop a regular triangular tiling, as in figure 80. There are infinite possible designs that can be used to create a hexastix model, but is good to start with simple polygons before moving on to more complex designs.
Figure 68: Hexastix designs on 2D grid.
Hexastix can be made with a different pattern on each axis, but this will cause the arrangement to have less symmetry. Not all of the possible patterns create stable hexastix arrangements that hold themselves apart in each direction. Comparing patterns using templates can be a useful way to save time and materials, but is not usually necessary for simple hexastix investigations.
Figure 82 : Hexastix 28 sticks template.
Figure 83: Hexastix grid on truncated octahedron.
To plot a chosen pattern onto a hexastix arrangement, the design is first placed on a grid at just one of the 4 axes before being translated 180 degrees across from the original design, this is then mirrored and rotated 180 degrees to map the pattern onto the remaining 2 axes as in figure 82. Many polygons have multiple possible orientations in relation to the hexastix grid. To avoid having to consider all of the permutations, while also maintaining symmetry, it can be helpful to keep the structure oriented to an elected top and bottom along the 4-fold axis.
Figure 84: Hexastix with paper template.
Figure 85: Hexastix 96 pencils.
Next, we will be looking at even more complex hexastix geometry before moving on to tristix.
copyright 2022 Anduriel Widmark
16- Hexastix grids.