Top > Science > Math > Recreations > 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.

» 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.

» Solomon W. Golomb - Home Page of the inventor of polyominoes. Includes biography, black and white picture, research interests and publications list.

» 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.

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