Polyominoes

• Gerard's Universal Polyomino Solver   - 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].

• Animal Enumerations - Enumeration on regular tilings of the Euclidean and Hyperbolic planes.
• Anna's Pentomino Page - Anna Gardberg makes pentominoes out of sculpey and agate.
• Arnab's Pentominos Puzzle - Fast Pentominos puzzle solver, works on DOS/Windows platform. Free downloads.
• Blocking Polyominos - Rodolfo Kurchan searchss the smallest polyomino such that a particular number of copies can form a blocked pattern. With solutions.
• Canonical Polygons - Ronald Kyrmse investigates grid polygons in which all side lengths are one or sqrt(2).
• Christopher Monckton's Eternity Puzzle - 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.
• Counting Horizontally Convex Polyominoes - Journal of Integer Sequences, Vol. 2 (1999), Article 99.1.8. Defines and counts horizontal convexity.
• Cynthia Lanius' Lesson: Polyominoes Introduction - From tetris to hexominoes, Cynthia explains them in color.
• Dancing Links - Don Knuth discusses implementation details of polyomino search algorithms (compressed PostScript format).
• Equilateral Pentagons - Jorge Luis Mireles Jasso investigates these polygons and dissects various polyominos into them. Animations show cases of infinite solutions.
• Eternity Page - Alex Selby's page with a description of his solution method, with illustrations in .png and .pdf files.
• Flexagons - Conrad and Hartline's 1962 article on Flexagons.
• Gamepuzzles - Polyomino and polyform games and puzzles manufactured by Kadon Enterprises Inc.
• The Geometry Junkyard: Polyominoes - Numerous links, sorted alphabetically.
• Gerard's Pentomino Page - Illustrates the 12 shapes. symmetrical combinations.
• Golygons - Harry J. Smith's explains polyominoes with consecutive integer side lengths.
• Golygons by Mathworld - What they are, and how to find them.
• Harold McIntosh's Flexagon Papers - Including copies of the original 1962 Conrad-Hartline papers. Abstract, html-pages, or .pdf documents.
• Henri Picciotto's Geometric Puzzles in the Classroom - Polyform puzzle lessons for math educators to use with their students, including polyominoes, supertangrams, and polyarcs.
• Information on Pentomino Puzzles - At the Combinatorial Object Server.
• Isoperimetric Polygons - Livio Zucca tiles polygons of equal perimeter, or isoperiploes.
• Java pentominoes - Thery families web site with pentomino solver. (English/French)[Java].
• Knight's Move Tessellations - Dan Thomasson looks at tesselations with numerous unexpected shapes traced out by knight moves.
• Lego Pentominos - Eric Harshbarger. This puzzle maker says that the hard part was finding legos in enough different colors.
• Livio Zucca's polyomino-covered cube - Colorful illustrations demonstrate how closed surfaces could be covered by polyominoes.
• Logical Art and the Art of Logic - Pentomino pictures, software and other resources by Guenter Albrecht-Buehler.
• The Mathematics of Polyominoes - Kevin Gong offers download of his polyominoes games shareware for Windows and Mac. 100 boards are included. A Java version is under development.
• Mathforum : a Pentomino Problem - Geometry Forum: Lists the pentominoes; fold them to form a cube; play a pentomino game. (project of the month, 1995)
• Mathforum : Minimal Domino Tiling - Tiling a square without cutting it into two.(Problem of the week 826, Spring 1997)
• Mathforum : Tiling Rectangles from Ell - Stan Wagon asks which rectangles can be tiled with an ell-tromino.
• Maximum Convex Hulls of Connected Systems of Segments and of Polyominoes - Bezdek, Brass, and Harborth. Abstract to an article which places bounds on the convex area needed to contain a polyomino. (Contributions to Algebra and Geometry Volume 35 (1994), No. 1, 37-43.)
• Miroslav Vicher's Puzzles Pages - Polyforms (polyominoes, and polyiamonds) graphics, tables and resources (English/Czech).
• My Polyomino Page - Michael Reid's numerous articles on polyominoes and tilnig, with references and links.
• Packing Polyominoes - Mark Michell investigates packing pentominoes into rectangles of various non-integer aspect ratios in order to obtain the largest possible pieces using straight cuts.
• Packing Shapes - Erich Friedman's Introduction to a variety of packing and tiling problems.
• Pairwise Touching Hypercubes - Erich Friedman's problem of the month asks how to partition the unit cubes of an a*b*c-unit rectangular box into as many connected polycubes as possible with a shared face between every pair of polycubes. Answers provided.
• Pentamini Pentaminos Pentominoes - A container of mathematical games, gadgets and software. (English/Italian)
• Pento - Amamas Software offers a pentomino solving software.
• Pento-Mania - Pentomino based puzzle game lets children solve and create geometric puzzles. Win32 software, try or buy.
• Pentomino Applet - Rujith de Silva's applet puzzle offers games of four different sized rectangles. Source code available. [Java]
• Pentomino Applet - Fill up a given area using pentomino shapes, rotating and flipping them. Three levels of difficulty.[Java].
• Pentomino Covers - Problems on minimal covers.
• The Pentomino Dictionary by Gilles Esposito-Farèse - English words that can be written using the pentomino name letters FILNPTUVWXYZ and other related curiosities, including a homage to Georges Perec. (English/French).
• Pentomino Dissection of a Square Annulus - From Scott Kim's Inversions Gallery.
• Pentomino Homepage - Lorente Philippe's site describes the building blocks, nomenclature, solutions, and numerous games. (French/English)
• Pentomino HungarIQa - Kati presents a pentomino puzzle using poly-rhombs instead of poly-squares. [English/French/German/Hungarian]
• Pentomino Puzzles. - Pentomino solver with download. Windows 95 and later required. [German/English]
• Pentominoes - Expository paper by R. Bhat and A. Fletcher. Covers pre-Golomb discoveries. the triplication problem and other aspects.
• Pentominoes : an Introduction - Centre for Innovation in Mathematics Teaching presents colourful examples of many tiling problems, duplication, triplication, etc.
• Pentominos - B. Berchtold's applet helps tile a 6x10 rectangle. [German]
• Pentominos - Graphics problems, solutions (including animated GIF) and links. (English/German through main page)
• Pentominos Puzzle Solver - David Eck's graphical solver applet uses recursive technique. Source code available. [Java]
• The Poly Pages - About various polyforms - polyominoes, polyiamonds, polycubes, and polyhexes.
• Polyform and Dissection Puzzle Links - Christian Eggermont's link page.
• Polyform Spirals - Jorge Luis Mireles explains finite and infinite spirals made up of polyforms.
• Polyforms - Ed Pegg Jr.'s site has pages on tiling, packing, and related problems involving polyominos, polyiamonds, polyspheres, and related shapes.
• Polygon Puzzle - Open source polyomino and polyform placement solitaire game.
• Polyiamond Exclusion - Colonel Sicherman asks what fraction of the triangles need to be removed from a regular triangular tiling of the plane, in order to make sure that the remaining triangles contain no copy of a given polyiamond.
• Polyiamonds - Mathforum. This Geometry problem of the week asks whether a six-point star can be dissected to form eight distinct hexiamonds.
• Polyomino and Polyhex Tiling - Joseph Myer's tables of polyominoes and of polyomino tilings, in Postscript format.
• Polyomino Applet - Wil Laan's applet searches for solution of packing hexominoes into more than 45 different shapes.[Java]
• Polyomino Enumeration - 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.
• Polyomino Fuzion Game - Puzzles using pentominoes and hexominoes. Fuzion, game that designs and (semi-)automatically finds solutions. Links.
• Polyominoes - Describes a numerical invariant that can be used to classify polyominoes.
• Polyominoes - Introduction to Tetrominoes, Pentominoes, Hexominoes, Heptominoes, Octominoes, Fixed (translation only) Polyominoes. Numerous Links.
• Polyominoes: Theme and Variations - Jankok presents information about filling rectangles, other polygons, boxes, etc., with dominoes, trominoes, tetrominoes, pentominoes, solid pentominoes, hexiamonds, and whatever else people have invented as variations of a theme. References included.
• Polyominoids - Jorge Luis Mireles Jasso presents connected sets of squares in a 3d cubical lattice. Includes a Java applet as well as non-animated description.
• Polypolygon Tilings - S. Dutch discusses polyominoes, poliamonds, and polypolygons with special attention to tiling characteristics.
• Primes of a 14-omino - Michael Reid shows that a 3x6 rectangle with a 2x2 bite removed can tile a (much larger) rectangle. It is open whether it can do this using an odd number of copies.
• Puzzle Fun - Newsletter edited by Rodolfo Kurchan about pentominoes and other math problems.
• Rectifiable Polyomino - Karl Dahlke explains and demonstrates tiling. Includes C-program source.
• Schröder Triangles, Paths, and Parallelogram Polyominoes - A paper on their enumeration by Elisa Pergola and Robert A. Sulanke.
• Six Squares Problem - This Geometry Forum problem of the week asks for the number of different hexominoes, and for how many of them can be folded into a cube.
• The Soma Cube - Soma-solving program in QBASIC by Courtney McFarren.
• Somatic - A solver for arbitrary polyomino and polycube puzzles. Binary code and source downloads available.
• Sqfig and Sqtile - Eric Laroche presents computer programs for generating polyominoes and polyomino tilings. Includes source codes in C, and binaries.
• Taniguchi's Programs - Windows software to solve polyiamond and sliding block puzzles.
• Tesselating Locking Polyominos - Bob Newman examines the history of the subject and presents his minimal solutions.
• Thorleif's SOMA Page - SOMA puzzle site with graphics, newsletter and software.
• The Three Dimensional Polyominoes of Minimal Area - 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).
• Three Nice Pentomino Coloring Problems - Alexandre Owen Muñiz presents the Icehouse set which lends itself to different polyomino coloring games.
• Tiling a Square With Eight Congruent Polyominoes - Michael Reid's abstract of a paper in the "Journal of Combinatorial Theory, Series A".
• Tiling of Pythagorean Triplets - Joe Fields suggests that L-decomposition of squares of Pythagorean triplets could always be tiled.
• The Tiling Puzzle Games of OOG - Mr. Confetti presents a Windows and Java game for tangrams, polyominoes, and polyhexes.
• Tiling Rectangles and Half Strips with Congruent Polyominoes - Michael Reid's abstract of paper in the "Journal of Combinatorial Theory, Series A".
• Tiling Stuff - Jonathan King examines problems of determining whether a given rectangular brick can be tiled by certain smaller bricks. Includes numerous articles in .pdf format.
• Tiling with Notched Cubes - Robert Hochberg and Michael Reid exhibit an unboxable reptile: a polycube that can tile a larger copy of itself, but can't tile any rectangular block. Abstract of article to "Discrete Mathematics".
• Unbalanced Anisohedral Tiling - 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.
• Unbeatable Tetris - Java applet demonstres that this tetromino-packing game is a forced win for the side dealing the tetrominoes. Complete with mathematical proof. [Java]
• Unfolding the Tesseract - Peter Turney lists the 261 polycubes that can be folded in four dimensions to form the surface of a hypercube, and provides animations of the unfolding process.
• What is a Golygon? - Harry Smith describes Dr. Dewdney's article in the July 1990 Scientific American's Mathematical Recreations column.
• Xominoes - Livio Zucca finds a set of markings for the edges of a square that lead to exactly 100 possible tiles, and asks how to fit them into a 10x10 grid.