- 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.
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.
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 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)
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.
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 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)
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: 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.
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.
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).
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.
Suggested link
Travel in Italy A guide for your vacation in Italy: hotels and hostels, bed and breakfast, resort, apartments and lodging with online prenotations. All you need to know to enjoy your trip in Rome, Florence, Venice or Naples: transportation, travel guides, travel services, train, airplane fares, museums, maps and views, shopping, recreation and sports, arts and entertainment... www.travel-in-italy.info
The Best and Cheapest Online Pharmacy - Free Shipping Worldwide!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.
George Huttlin's Puzzle Page - George Huttlin shares some ramblings in the world of polyominoes.
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.
Hexiamonds - George Huttlin explains and illustrates these shapes composed of 6 equilateral triangles, which in turn tiles different forms.
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.
