10-7-2022

Sticks in 6 Directions

There are an infinite number of ways sticks can be arranged in space, but there is a surprisingly limited number of ways that sticks can be symmetrically arranged. This blog has considered symmetric arrangements with elements parallel to only 3 and 4 directions, but now let us add some complexity and look at a few arrangements with icosahedral symmetry and 6 directions (figures 123-126).

Figure 123: 6 way packing.

Figure 124: 6 way packing.

Figure 125: 30 Sticks.

Figure 126: 30 sticks FIT.

Arrangements of 30 sticks were made with glass and the ends were joined to create 10 symmetrically linked triangles, shown in figure 127.

Figure 127: 10 triangles.

60 sticks can be joined in a similar way to create a structure of 20 linked triangles, as in figure 128.

Figure 128: 20 triangles.

Puzzlingly, the symmetric arrangements with icosahedral symmetry can be expanded further to have 12 or 24 axes, adding even more directions. With any luck, the direction you decide to take will lead to unexpected and bewildering places.

Figure 129: 30 sticks group. .

In the next blog post, we take a look at how we got to here, by way of the amazing work by the many people who have led the way, with a polystix blog bibliography.

copyright 2022 Anduriel Widmark