Kate always wears this necklace at shows, and so many people kept asking for it that here it is, by popular demand. The 12 quint shape miniatures, .5 inch unit squares, in handcrafted wood attached to a gold-tone chain, actually fit together to form a rectangle (not while being worn, of course). Great conversation piece, always a big hit at conventions. One size fits all. Each is a different combination, until we run out of solutions that have no enclosed piece. $49 (Shipping discount)

Something different...this one's full of holes—polyominoes sizes 2 through 4 with all the possible positions of two holes in the centers of their squares. Six single squares without holes complete the 10x10 tiling. Each size has its own color, so a fun and easy puzzle is to create interesting symmetrical patterns. A harder challenge is to arrange the pieces so every row, column and long diagonal contains exactly 5 holes. An even harder challenge is to get all the holes into a connected group. This two-dimensional set goes 3-D in the stacking puzzles, where in multiple levels holes go all the way through. Made in four combinations of transparent colors, like stained-glass, Fill-Agree comes with an easel for a light-catching display in its 11˝" tray. For ages 8 to adult, 1 or 2 players. $72

The five squares of the 12 pentominoes have been stretched diagonally into diamonds, or rhombuses (rhombi, to you purists). Since you can stretch them in two directions—along the short and long diagonal—you get 20 shapes in all. Perfect for filling a 10x10 rhombus-shaped tray. We've colored the pieces strategically with only 3 colors to allow total color separation (unique solution shown here, verified by Brendan Owen's computer program) and total color grouping, and a fine spectrum of challenges besides. They make surprising shapes outside the tray as well, including color symmetries. Be forewarned that these can be quite hard for even the easiest assemblies and the most expert solver. Those angles can fool the eye and mind. Available in two color combinations, with its own display stand. For ages 16 to adult, 1 to 4 players. $72

See a different set of rhombic pentominoes by László Nagy

The little brothers of Rhombiominoes—sizes 1 through 4 squares turned into rhombi, and each size gets its own vivid color. Originally made only as a limited-edition gift exchange for the International Puzzle Party of 2006, by name of Boston T-Party, this novel polyrhomb set has acquired permanent status and invites the building of hundreds of cool patterns, plus a fine spectrum of special challenges, including a handsome alphabet. You can also mix and match them with the Rhombiominoes set for larger constructions. Lasercut acrylic in 9x6" tray. For ages 6 to adult, 1 to 4 players. $45

For years, a search was on to find the fewest number of pieces, of whatever shape, that could form all 12 pentominoes and all 5 tetrominoes. Several world-class puzzlers attempted such a dissection, getting the number down to 9 and even 8 pieces. The 8 contained several duplicates, so were not entirely satisfactory. George Sicherman came up with 9 pieces, no duplicates, and won our Gamepuzzles Annual Pentomino Excellence award for 2019. We were thrilled to publish it with many other features added, such as convex, concave, symmetrical, and whimsical silhouette figures like the two shown at left, and 2 games. Its booklet contains a more detailed and fascinating history of dissection puzzles. Here's a little gallery of special challenges. Black tiles are supplied in pouch with a soft, gray velour 12x12" game grid. For 1 or 2 players, age 10-adult. $39

The uniquely checkerboarded, 2-sided pieces are the 12 pentominoes plus a 2x2 square. They fill the 8˝" tray as an 8x8 checkerboard in 1,294 ways and serve for dozens of other puzzles plus three games. Two of the more stubborn puzzles are "the longest river"—forming a single band of one color—and the "uncheckerboard", where you try to have no single squares of a color. The pieces are handfitted with 128 individually inlaid squares from laser-cut acrylic. For Quintachex's "second" silver anniversary in 2015, we gave them glistening silver colors: sizzling, hot, cool, and elegant. This set is suitable for 1 to 4 players, ages skilled 10 to adult. $95