Pentarose is a beautiful puzzle, made by Kadon Enterprizes, constructed using tiles from Penrose set P1. Penrose tiles can completely fill a plane, leaving no gaps. Unlike other tilings, they do not necessarily repeat any pattern, no matter how far out toward infinity they extend. The tilings assembled from them produce a vaguely five-fold symmetry, and the "golden ratio" is seen repeatedly. For true Penrose tiles, markings are placed on each tile that, when matched edge-to-edge, prevent periodic tiling. Since this set lacks the markings, the pieces can also be assembled in periodic designs.

The MathWorld page on Penrose tiles shows only the kites and darts, but mentions the two other groups of Penrose tilings, as well. Penrose's three sets are P1, or the pentacles, P2, or the kites and darts, and P3, or the rhombs. The same thick (72 degree) and thin (36 degree) rhomb shapes as are found in the P3 set are seen in the Deka-Star gamepuzzle, described below (see May 24, 2004).

The Pentarose puzzle shown here is a special edition made with transparent colored Lucite, with a translucent tray bottom, so light can shine through. There are many possible solutions to this puzzle that fit inside the tray; a page included with the puzzle gives various suggestions, and names the various shapes (mouse, airplane, cloverleaf, poplar leaf, and maple leaf). The pieces can also, more easily, be assembled free-form, without the tray.

While my seven-year-old loves the Deka-Star tiling puzzle, the Pentarose puzzle is too difficult for him to assemble. It's best for adults, while the Deka-Star is good for both adults and kids.

(Click on the images for a larger view.)