Tilings and Designs — Page 3 of  4

...created by Anneke Treep

Here's a novel concept: 24 diamond-shaped tiles and 6 triangular tiles carry the 6 dominant rainbow colors in every combination (one sample shown at right). Join them so colors meet only their own shades or their neighbors in the spectrum. Patterns emerge as you rearrange the tiles. Illustrated booklet shows many interesting shapes to solve outside the 8" tray, as well. It's proven to be one of our instant hits for all ages, 5 to adult. All acrylic, for 1 or 2 players. $65

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...created by Jacques Ferroul

The 27 tiles are transformations of a diamond into combinations of straight, convex, and concave sides. Though each piece has a unique shape, the set can be coaxed into finding the right neighbors to fill the desired space. With thousands of combinations possible (see samples below), the set lends itself to your most beautiful artistic creations. Jacques defined the colors by the pieces that are larger, smaller, or equal in area to the original diamond. The solution at left is rare: no two of the same color share sides. A strategy game is included, "Color Reefs", reminiscent of crabs' favorite hangout, coral reefs. Lasercut acrylic in 9" hexagonal tray with star grid, 18 lens-shaped black fillers, and a 12-page activities booklet. For 1 or 2 players, ages 8 to adult. $65

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Larger image of Grand Tans
and a couple of solutions

...over a hundred years of challenge

7 finely crafted hardwood pieces (not tangrams) form 101 fine figures. This puzzle was first published by F.A. Richter in Germany in 1891. We have reconstructed all their original puzzle figures and added a few new ones. In drawstring pouch it's also a fine travel game, for ages 8 to adult. $39

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How cool is this? This solution can easily transform into any tetromino (the 5 shapes made of four squares), also known as Tetris pieces. If old Archie only knew!

ARCHIMEDES' SQUARE—uniquely tricolored by Kadon
...described by Archimedes (circa 260 B.C.); see the video

This 14-tile dissection is the oldest documented puzzle in the world, and the decipherment of Archimedes' rediscovered manuscript is a hot topic among historical scholars and mathematicians. Also known as the Stomachion, it even made the front page of the New York Times, December 14, 2003. Luminous transparent colors in a sculpted 7" acrylic tray. Long unanswered:  Just how many ways can this square be solved? On October 31, 2003, Bill Cutler's program found the full answer of 536 distinct solutions. (Read the full story.) How many other convex shapes can the 14 tiles make? Bernd Rennhak in Germany found all 637 solutions. He also found that the set can solve 13 of the 14 tetratan shapes. The permutations are staggering. An amazing fact is that each tile's area is a whole number, based on the square as a 12x12 matrix. That gives each of the 3 colors an equal share of the total area. Here truly is ancient genius made visible. Some of the tiles' angles have sharp points, so we recommend ages careful 10 to adult.$42

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TRICOLOR STOMACHION MONOGRAPH, documenting the exhaustive study and analysis of all 1072 solutions by category, complete with illustrated Catalog of solutions and a Concordance for cross-reference. Read the amazing story of how three avid researchers pushed the frontier forward on this 2,200-year-old puzzle first studied by Archimedes. Co-authored by Joe Marasco, Kate Jones and Alex Streif, you can now order your very own copy on luxurious parchment-like paper, with color illustrations.     $10.72

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When purchased together with the Archimedes' Square ($42), the Monograph is only $5, total    $47

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Challenge open to the world: Find a convex or symmetrical figure not yet discovered, and we'll send you a little prize.
...designed by Serhiy Grabarchuk, extended by Kate Jones

This 7-tile square was inspired by the dissection patterns of Stomachion (see Archimedes' Square, above), the Diamond Puzzle of T. A. Snider, and the classical Tangrams. Tangramion has amazing properties of its own. One big surprise was that the square has only 10 solutions, compared to Stomachion's 536. To date, 93 convex shapes have been identified and solved. Only 33 mirror-symmetrical and 36 rotationally symmetrical shapes have turned up so far—partly due to the fact that none of the 7 tiles themselves is symmetrical. See these and many other clever and creative designs in the Tangramion booklet (.pdf file, 303KB). In warm Lucite colors of ruby, amber, topaz, in sculpted 7x7" tray. Color mix may vary. Endlessly entertaining and challenging for one player, ages 8 to adult.$42

Tangramion is a trademark of Serhiy Grabarchuk.

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SHADOW PLAYTM   created by Parakum Maitipe

Nine geometric shapes form imaginative designs and can be used to test for and develop creativity. Black acrylic pieces in their little drawstring pouch are handy to take on trips. Because these are not a puzzle to solve but a tool for creating recognizable images, their use also encourages communication and provides artistic fun for ages 6 to adult. Can you guess? At left, boy with toy boat; at right, a fort. (Shipping discount) $12

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...created by Jeremiah Farrell, extended by Kate Jones

This ingenious puzzle was presented by Jerry originally to the International Puzzle Party in Prague in 2008, under the name "Prague Six." The challenge was simply to combine the 8 right isosceles triangles and 8 "sheds" to form 1, 2, 3, 4, 5 and 6 squares with a unique rule: each square had to be "traceable". All four sides had to be exposed, either on the outside or the inside, or a combination of the two. No two squares could have tiles stuck together by a joined side. (Can you see all 18 squares in the sample at right? The 5 enclosed empty spaces also count as squares.) Curious minds have since then found solutions for every size up through 26 squares, each time using all 16 tiles, with or without the tray. New solutions win fame. Exceed 26 and win a prize. In the spirit of the classic tangrams, countless fancy figures and designs are possible when not bound by the traceable-squares rule. Two friendly games are included. With 7" tray. Recommended for ages 8 to adult, 1 or 2 players. $42

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We've found some of the most marvelous books of geometric patterns, with polygons dancing in symmetrical formations that evoke the creative imagination. These four volumes of Images, geometric tilings by Roger Burrows, contain an infinity of hidden scenes, forms, patterns, potentialities. They stimulate visual creativity. Each book is 9"x9", with 48 sheets per book. Pages within a book repeat so you can experiment with variations. Each volume is a new and fresh collection. Each, $7

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