Figure 41: Tetrastix boxes.
Models of tetrastix can be thought of as finite subsets that lay on an infinite tetrastix arrangement. The geometry of a tetrastix models can efficiently be designed in 2-dimensions, as each axis lays on the simple cubic lattice in a regular way.
Figure 42: Square grid.
To start designing tetrastix, patterns can be drawn on square graph paper, as in figure 26. There are infinite possible designs that can be used to create a tetrastix model, but it is good to start with simple polygons before moving on to more complex designs.
Figure26: Polygon designs on square grid.
Novel designs can be placed onto a square grid that represents the 3 directions of a tetrastix, e.g. figure 44. To plot a chosen pattern onto a tetrastix arrangement, the design is placed on one of the 3 axes and then rotated 90 degrees, (perform a transformation) and placed onto the other axes of a tetrastix.
Figure 43: Tetrastix cube template.
Figure 44: Tetrastix template half.
Tetrastix can be made with a different pattern on each axis, but the arrangement will have less symmetry. Not all of the possible patterns create stable tetrastix arrangements that hold themselves apart in each direction. Comparing patterns using templates (figure 44) can be a useful way to save time and materials but is not usually necessary to employ a template for creating simple tetrastix arrangements.
Figure 45: Tetrastix detail.
Figure 46: Tetrastix detail.
Next, we will work out more tetrastix geometry before moving on to hexastix.
copyright 2022 Anduriel Widmark
10- Tetrastix grids.