Above are just a few samplings of the octagonal patterns that you can make with the Triangoes Jr. set. Some have diagonal symmetry, some have vertical symmetry, and some even have "rotational" symmetry. Notice that in some designs the two colors are opposite each other, like yin and yang. Those are some of the most challenging images you can create with Triangoes Jr., especially those that have several types of symmetry at the same time. And there are hundreds of other shapes to make.
Solvers of the above patterns include Jason Garcia (right), Manuel Garcia, Kate Jones, Tom Rankin and Joyce Deitschmann.
Jason also contributed these additional handsome symmetry patterns. You can see what colors his personal sets have!
Some rare patterns can have each color forming a single connected area, and both colors are the same shape. In a contest offered by the Dutch puzzle journal, Cubism For Fun, several such congruent color solutions were discovered by Paul van Leeuwen, Helmut Postl, Franz-Josef Schulte, Jack Sobel and Christian Halberstadt. The first one was also discovered about 10 years earlier by Andy Liu. Here are all the patterns known to date::
If you find any new patterns for this group, or prove there are no others, let us know!
Here's an expanding collection of unusual designs with mirror, diagonal, and opposite-color symmetries. Then we show a new theme of letters defined by color, created by Meshele Merchant. More will be added as they are discovered. These solutions are by Meshele, Eric and Kate.
Another challenge is to form two mini-octagons simultaneously. This pair has similar but opposite color patterns and maximizes one color. Too bad their borders can't be all the same color. There are many other variations. Creating opposite-color designs like these is tricky.
Here are a few more complementary pairs:
Jack Heaney, a friend, customer and long-time puzzle lover, has found an amazing yin-yang color solution to the pairs challenge. It's posted on his webpage, Polyanimals. Jack also proved the pair can't be solved with color-matching, either.
Finally, there's no end to the fun shapes you can create with the colors. For starters, here's a fish. We'll add more critters here as we find them.