Puzzles

Puzzles

As shown on the Penrose Tiling page, phi is the basis for shapes called kites, darts and diamonds that can create five-fold symmetry, which was thought impossible until the 1970's.

You can explore the beauty of design with this symmetry as well as other golden, phi-based proportions with the puzzles below available from Kadon Enterprises.

PENROSE KITES & DARTS

Sir Roger Penrose's patented quadrilaterals form non-periodic symmetries (no regularly repeating patterns) out to infinity. They're sold in pods: each pod contains 5 kites, 3 darts. The all-acrylic tiles measure 1.25 inches on their longer sides. Later on we plan to add a gameboard and a fascinating strategy game for two players to the two larger sets. By the way, the nicknames, kite and dart, were appended to these shapes originally by the brilliant and dynamic mathematician, John Horton Conway, who also invented "The Game of Life."

PENROSE DIAMONDS

If these thick and thin diamonds had special markings on them to force certain adjacencies, they would represent Penrose's patented concept. We've left them blank so they can do Penrose's non-periodic tilings plus attractive kaleidoscopic variations. Each pod: 5 thick, 3 thin diamonds. These are the tiles seen on the cover of Discover magazine a few years ago.

Penrose Kites and Darts and Penrose Diamonds are made
by Kadon under exclusive license from
Pentaplex Ltd., Brighouse, UK

COLLIDESCAPE^TM
....the golden triangles

Two isosceles triangles have the interesting properties of forming ever larger models of themselves, and of modeling any parts of pentagon tilings. For example, two of the "wide" triangles joined on their long side form a thick Penrose diamond. Joined on their shorter side, they form a "dart." Join two of the taller triangles at their base and you get a thin Penrose diamond. Join them on their longer side and get a "kite". Much of this research was done by Ward Hollins, who named them "Collidescape" for their kaleidoscopic symmetries and non-periodic tiling elusiveness. Each pod: 5 wide, 3 tall triangles.

PENTAROSE^TM

Pentarose is surely one of our most gorgeous art puzzles. Transformed pentagons and sections of stars are the very shapes that fit together without leaving holes. They are based on prototiles discovered by Sir Roger Penrose during research into non-periodic tilings. We've styled it in four luminous acrylic colors in an 11" circular tray, with a small easel included. Recommended for ages 12 to adult.

Pentarose was developed and is made by
Kadon under exclusive license
from Pentaplex Ltd., Brighouse, UK

Puzzling Pentagon

PUZZLING PENTAGON^TM
...posed by Donald Knuth

This 16-piece lasercut acrylic puzzle has a lengthy pedigree. From a suggestion by Nob. Yoshigahara, the well-known Japanese puzzlemaster, to the posing of 4 very difficult questions by Don, this puzzle was first distributed at an International Puzzle Party. We developed it further, adding many other designs and questions. There's always something else to explore with it. There are 4 triangle sizes each in 4 colors, which can build 4 separate little pentagons or one large one. Their geometry is related by the "golden ratio." Handy cloth storage bag and instructions are included. Recommended ages 10 to adult.

DEKA-MOSAIK^TM developed by Kate Jones

This set is an excellent introduction to pentagon play: Create ever-changing patterns with 15 pairs of golden triangles and 5 pentagons in an acrylic 7" decagon tray. The four-color mix of the pieces makes it fun to continue to find new and different arrangements. Colors may vary. Recommended for ages 8 to adult.

DEKA-STAR^TM styled by Kate Jones

This set of two shapes in four colors is the next best thing to a kaleidoscope. The 36-degree rhombus and the 72-degree rhombus are just what it takes to fill up a decagon. Vary the patterns as you like from utterly chaotic to exquisitely symmetrical. Colors may vary from those shown and may change periodically. Recommended for ages 6 to adult.

KITE-MOSAIK^TM developed by Kate Jones

This set is the most complex of the decagon trilogy. Four shapes in four colors include kites, darts, and the two golden triangles. Kite patterns of various sizes can be formed with the colors within the tray. Outside the tray the pieces can model every size of kite, from a unit tile to a giant one that exactly uses the entire set. Build it a certain way, and you can split it to form two tall triangles. Join those a different way to form a thin diamond. We got quite a kick out of discovering these relationships, maybe because solving the shapes was really tough. Color mix may vary. Recommended for ages 10 to adult.

Kadon Enterprises, Inc.
(410) 437-2163