SD701 Open Directory

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.




» Blocking Polyominos - Rodolfo Kurchan searches 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).




» 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 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.




» Hyperbolic Planar Tessellations - Don Hatch's page on hyperbolic tesselations with numerous illustrations.




» Information on Pentomino Puzzles - At the Combinatorial Object Server.




» 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.




» 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 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.




» 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]




» Pentomino Relationships - Symmetries in the families of rectangular solutions.




» 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 Curiosities - Topics include exclusion, compatibility, and wallpaper. Includes examples and charts.




» 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.




» Polyomino and Polyhex Tiling - Joseph Myer's tables of polyominoes and of polyomino tilings, in Postscript format.




» 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.




» 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.




» 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.




» 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.




» 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.

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