Polyforms are phenomenal in how they can fit together to build larger figures, to fill the plane without holes, and to form symmetrical and congruent shapes.

The exploration of polyform puzzles has a long history, dating back to the 1920s. The mathematical names for the various types have usually been introduced by their respective investigators.

Solomon Golomb started the trend in 1953 with polyominoes (see also More about polyominoes and polycubes).

Shapes made of equilateral triangles became polyiamonds, from diamond, made of two triangles. Shapes made of hexagons are simply polyhexes, and shapes made of isosceles right triangles are polytans, from their resemblance to tangrams. In the literature polytans are sometimes also referred to as "polyaboloes."

Kadon has been making polytan sets since 1988, privately distributed but not offered to the general public, because these sets were thought to be much too difficult for casual fun and recreation. For the determined solver, we are happy to make them available. Here, then, are our Tan Tricks sets, sizes 1 through 6. Someday we'll even publish an extensive book of activities for them.

A nicely simplified version of this group is the Shape by Shape set we sell in the Puzzles section, made by ThinkFun, Inc. (formerly Binary Arts) from a design by Nob Yoshigahara. Nob used our Tan Tricks during his research.

Extending the research

Col. George Sicherman's website presents a section on "Polyform Curiosities", investigations into the esoteric problems of exclusion, compatibility and oddities, with examples and solutions.

Solution programs

Solutions for puzzles of this type can now be derived by computer. Aad van de Wetering from the Netherlands has written a fine and quick program for solving figures with polyominoes, polyiamonds and polyhexes. You can download it from his website.

Eric Postpischil has written a nice TriSolve program for solving any polyiamond figure, downloadable from his website.

Andrew Clarke is one of the great polyformists of this century, a legend in his time for amazing, beautiful, difficult and huge solutions. He is now presenting much of this material on a website he calls simply The Poly Page. It's a great reference site, done with style and intelligence.

David Goodger has an enthusiastic polyform project and solving programs on Polyform Puzzler and shows solutions with very attractive colorful graphics. He has generously made his solving program available as freeware and is constantly upgrading it to make it more versatile and adaptable to new types of polyforms as they become defined.

Innovations

And the process of discovery continues. Alan Schoen invented rombiks, shapes made of one or two rhombuses joined in circle tilings.

Kate Jones introduced polyrhombs, for polyominoes formed of rhombs rather than squares, and roundominoes, for circles joined on a square grid.

Henri Picciotto created polyarcs, formed of convex and concave curves and straight edges.

Jacques Ferroul contributed polyspidrons that combine triangles and spirals. The latter are by way of being "poly-multiforms," combining more than one kind of building block. Jacques' Stelo is a neat small subset of the highly complex polyspidrons, without the curves.

Jacques also has discovered a huge collection of beautiful shapes to solve with his Tetrapentos, the 7-piece little brother to our Mini-Iamond Ring, using just the tetriamonds and pentiamonds. His website shows many silhouettes as new challenges. If you already own Mini-Iamond Ring, you can use it to explore and solve all those. Or get your own copy of Tetrapentos, in tray or pouch.

A new kind of multi-polyform is Jacques Ferroul's La Ora Stelo, using combinations of the two isosceles triangles related to the golden ratio. They've opened a whole world of new explorations. You can order them in the Pentagon Universe section.

Unusual relatives of polyforms are Kadon's Triangoes and Triangoes Jr., which combine the characteristics of both polyforms and edgematching color sets, and Cubits, created by Anneke Treep and Christian Freeling, with shapes of one, two and three diamonds joined in a cube-like color tiling.

New ideas are emerging continually. Stay tuned.

Our domain

Kadon is the world's pre-eminent producer of polyform puzzles for hands-on enjoyment and as a playable art form. In 2007 we procured the Internet domain name, polyformpuzzles.com, as a portal to our main gamepuzzles.com website and to its polyforms and polyominoes sections.