To begin this experiment, I first purchased two refrigerator-sized Fractiles-7 sets (available at http://fractiles.com/), and then, early on a Sunday, quietly arranged these rhombus-shaped magnets on the refrigerator in our apartment (population: 4, which includes two math teachers and two teenagers), using a very simple pattern.
Here’s a close-up of the center. There are 32 each, of three types of rhombus., in this double-set, for a total of 96 rhombic magnets, all with the same edge length.
The number of possible arrangements of these rhombi is far greater than the population of Earth.
The next step of the experiment is simple. I wait, and see what happens.
It should be noted that there is a limit on how long I can wait before my inner mathematical drives compel me to play with these magnets more, myself — but I do not yet know the extent of that limit.
Unlike my previous octagon-tiling discoveries (see previous post), this is a chiral, radial tessellation, with the colors chosen to highlight that fact.
In April 2014, I found a tessellation of the plane which uses two kinds of octagons — both types equilateral, but only one type regular.
Now, I have found two more ways to tessellate a plane with octagons, and these octagons are also equilateral. However, in these new tessellations, only one type of octagon is used. One of them appears below, twice (the second time is with reversed colors), and the other one appears, once, in the next post.
This tessellation is made entirely of octagons. Half of them are regular, while the other half are equilateral and tetraconcave.