In 2021, John Greening surprised us with this shapely figure built of the 66 octiamonds and added this note: "This is my favorite of all the sets and I call it the grandfather set because the set is balanced with even parity, there are no holes and all pieces tile the plane. 12fold symmetry is also possible with this set."
Congratulations, John. That is a thing of beauty, coaxing all different shapes into exquisite collaboration. And you solve these without a computer, so double wow.
At the end of October 2022, John Greening amazed us once again with this magnificent solution of a giant snowflake. It took him about a week to solve by hand, with a clever shuffle of the last six pieces. What a marvel! And a few months later, his superbly symmetrical Stars arrived. The Figure8/Infinity double ring greeted us in January 2024. Simply gorgeous!
On February 3, 2024, John Greening delighted us with this fancy snowflake solution, continuing the sixfold symmetry theme that the octiamonds naturally embrace. Notice the V in the very center.
In June 2024, even more elaborate Octiamond designs arrived from John's inventive labors to enrich our gallery: two triple rings, a sausage, and a stubby star.
A little later in June 2024, three more beauties arrived. The triangle and the lattice had taken John a few days each to solve. The star took him only about 5 hours.
And as dessert for his summer banquet of successes, John Greening sent two more exquisite stubby Star formations:
In midJuly 2024, John's ingenuity turned to pretty spaces and fancy contours, giving us hexagons with holes, and triangles with triangular holes, and a diamond with a center line of hexagons, and what he called a cloverleaf.And all formed with the tricky tiles of all different shapes of 8 triangles joined. One can only marvel at such solving prowess.
Then see partnerships of hexiamonds and octiamonds, where the smaller enclosed pieces also form precise doubled triamonds: the two triangles surrounding a center of three hexagons formed of hexiamonds, with point up and down and the hexagonal hexiamond in the very center. Next comes an order5 wavy diamond enclosing a row of three order2 hexagons. What a delight to know such solutions are even possible!
In September 2021, John Greening produced his most amazing result to date: the Hendekiamond Ring, consisting of 1186 different tiles, each 11 triangles in size. At this scale, even more pieces with holes showed up, and John succeeded in arranging all 38 holes (covering 52 unit triangle spaces) in symmetrical locations around the inner and outer perimeter. He even found solutions where the outer triangle holes point either in or out. It took John several months to construct this ring to fit exactly around the previous nested rings (see above), working with painstakingly handcut pieces.
Rumors came that John was already tackling the next size up—the order12 polyiamonds with 3,334 different tiles—is that a world record yet?—to be achieved by hand, not by computer. After several weeks, John completed the full ring, with symmetrical arrangements of the pieces with holes. Few humans can equal such a superachievement. To assist in his recording, John built a workboard six feet in diameter, showing the entire solution as it emerged. See the closeup of a smaller section below. See also a closeup of the section around 5 o'clock, where most of the chunky tiles cluster, John's strategy for grouping the easiest pieces for the last. Congratulations, John! You are our greatest winner.
