| Symmetrical solutions with 5 tetratans
This project was initiated by Tick Wang, a puzzle enthusiast from Shanghai, in January 2022, as an addendum to our Tan Tricks sets. If you already own the set, use the pieces shown and have fun solving. Even if you don't own the set, you can just make cardboard cutouts of these five shapes.
Tick examined the 14 tetratans of Tan Tricks I and set aside all the pieces that were convex or symmetrical. He was left with these five rather irregular tiles:
Tick's goal was to find all the symmetrical shapes that could be formed by 2, 3, 4, and all 5 of these tetratans. He noticed that certain two pieces always occurred, in every shape, and the question is: Can any 3- or 4-piece symmetrical shape be formed without including both of those pieces? Can you find a proof either way? The first solver to send us such a proof will win a prize. Our email address: Kadon Enterprises, Inc.
Here are a few sample solutions using 2, 3, 4, and all 5 pieces. Do you detect which two pieces are always present? Piece colors are shown as different for artistic effect only, to highlight each piece.
Further, there are 55 figures with holes enclosed, anywhere from a single triangle to 6 triangles.
Have fun solving these. Also see how many 3-piece and 4-piece symmetries you can find.
Here we show his huge collection of mirror and rotational symmetries for your visual pleasure. They start with 2 pieces of each color, then 3, 4, and all 5. See not only the interesting shapes the tiles will make but also the variety of spaces around them, including triangles, squares, parallelograms, trapezoids, stars, and even octagons. Isn't it amazing how many variations just 5 shapes can make, and even their symmetrical solutions can be rotated or exchanged to form even more permutations of a simple arrangement? Here is the wonder of mathematics formed into playable art. Enjoy the tour.
If you'd like to own a Tetra-Tray set (the 20 tetratan pieces in 6" tray) to work out these solutions or to discover your own designs, we'll be happy to custom-make it for you in lasercut acrylic for $29.
|Back to Tan Tricks I|