Science

Polyomino and polyform games and puzzles manufactured by Kadon Enterprises Inc.

Describes a numerical invariant that can be used to classify polyominoes.

Numerous links, sorted alphabetically.

Computes from 1 to 3.38 billion solutions with graphic display to each of the 60+ problems of different sizes and shapes. Pieces vary from pentominoes to heptominoes, sometimes in combination. Table summarizes properties and example solution of each problem. [Java required].

Rules, the solution by Alex Selby and Oliver Riordan, other resources and links. The puzzle is made up of 209 pieces of polydrafters, each one is a combination of 12-30/60/90 triangles.

SOMA puzzle site with graphics, newsletter and software.

Graphics problems, solutions (including animated GIF) and links. (English/German through main page)

Pentomino pictures, software and other resources by Guenter Albrecht-Buehler.

Pentomino based puzzle game lets children solve and create geometric puzzles. Win32 software, try or buy.

A solver for arbitrary polyomino and polycube puzzles. Binary code and source downloads available.

Journal of Integer Sequences, Vol. 2 (1999), Article 99.1.8. Defines and counts horizontal convexity.

David Eck's graphical solver applet uses recursive technique. Source code available. [Java]

Eric Laroche presents computer programs for generating polyominoes and polyomino tilings. Includes source codes in C, and binaries.

Expository paper by R. Bhat and A. Fletcher. Covers pre-Golomb discoveries. the triplication problem and other aspects.

Karl Dahlke explains and demonstrates tiling. Includes C-program source.

Including copies of the original 1962 Conrad-Hartline papers. Abstract, html-pages, or .pdf documents.

Conrad and Hartline's 1962 article on Flexagons.

Illustrates the 12 shapes. symmetrical combinations.

What they are, and how to find them.

Ed Pegg Jr.'s site has pages on tiling, packing, and related problems involving polyominos, polyiamonds, polyspheres, and related shapes.

Java applet demonstres that this tetromino-packing game is a forced win for the side dealing the tetrominoes. Complete with mathematical proof. [Java]

Joseph Myers and John Berglund found a polyhex that must be placed in two different ways in a tiling of a plane, such that one placement occurs twice as often as the other.

Anna Gardberg makes pentominoes out of sculpey and agate.

Kevin Gong offers download of his polyominoes games shareware for Windows and Mac. 100 boards are included. A Java version is under development.

Eric Harshbarger. This puzzle maker says that the hard part was finding legos in enough different colors.

Open source polyomino and polyform placement solitaire game.

Enumeration on regular tilings of the Euclidean and Hyperbolic planes.

L. Alonso and R. Cert's abstract of a paper published in vol. 3 of the Elect. J. Combinatorics. Full paper available in different formats (.pdf, postscript, tex etc).

B. Berchtold's applet helps tile a 6x10 rectangle. [German]

Rujith de Silva's applet puzzle offers games of four different sized rectangles. Source code available. [Java]

K. S. Brown examines the number of polyominoes up to order 12 for various cases involving rotation or reflections. Equations linking the cases are proposed.

About various polyforms - polyominoes, polyiamonds, polycubes, and polyhexes.

Polyforms (polyominoes, and polyiamonds) graphics, tables and resources (English/Czech).

English words that can be written using the pentomino name letters FILNPTUVWXYZ and other related curiosities, including a homage to Georges Perec. (English/French).

Don Hatch's page on hyperbolic tesselations with numerous illustrations.

Symmetries in the families of rectangular solutions.

Polyform puzzle lessons for math educators to use with their students, including polyominoes, supertangrams, and polyarcs.

Joseph Myer's tables of polyominoes and of polyomino tilings, in Postscript format.