Directory of Polyominoes Resources

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• Animal Enumerations

  http://www.ieeta.pt/~tos/animals.html
  Enumeration on regular tilings of the Euclidean and Hyperbolic planes.

• Anna's Pentomino Page

  http://www.geom.uiuc.edu/~summer95/gardberg/pent.html
  Anna Gardberg makes pentominoes out of sculpey and agate.

• Blocking Polyominos

  http://www.eldar.org/~problemi/pfun/blocked.html
  Rodolfo Kurchan searches the smallest polyomino such that a particular number of copies can form a blocked pattern. With solutions.

• Canonical Polygons

  http://sti.br.inter.net/rkyrmse/canonic-e.htm
  Ronald Kyrmse investigates grid polygons in which all side lengths are one or sqrt(2).

• Christopher Monckton's Eternity Puzzle

  http://mathpuzzle.com/eternity.html
  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

  http://www.cs.uwaterloo.ca/journals/JIS/HICK2/chcp.html
  Journal of Integer Sequences, Vol. 2 (1999), Article 99.1.8. Defines and counts horizontal convexity.

• Cynthia Lanius' Lesson: Polyominoes Introduction

  http://math.rice.edu/~lanius/Lessons/Polys/poly1.html
  From tetris to hexominoes, Cynthia explains them in color.

• Dancing Links

  http://www-cs-faculty.stanford.edu/~knuth/papers/dancing-color.ps.gz
  Don Knuth discusses implementation details of polyomino search algorithms (compressed PostScript format).

• Flexagons

  http://delta.cs.cinvestav.mx/~mcintosh/comun/flexagon/flexagon.html
  Conrad and Hartline's 1962 article on Flexagons.

• Gamepuzzles

  http://www.gamepuzzles.com/
  Polyomino and polyform games and puzzles manufactured by Kadon Enterprises Inc.

• Gerard's Pentomino Page

  http://www.xs4all.nl/~gp/pentomino.html
  Illustrates the 12 shapes. symmetrical combinations.

• Gerard's Universal Polyomino Solver

  http://www.xs4all.nl/~gp/PolyominoSolver/Polyomino.html
  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].

• Golygons by Mathworld

  http://mathworld.wolfram.com/Golygon.html
  What they are, and how to find them.

• Harold McIntosh's Flexagon Papers

  http://delta.cs.cinvestav.mx/~mcintosh/oldweb/pflexagon.html
  Including copies of the original 1962 Conrad-Hartline papers. Abstract, html-pages, or .pdf documents.

• Henri Picciotto's Geometric Puzzles in the Classroom

  http://www.mathedpage.org/puzzles/
  Polyform puzzle lessons for math educators to use with their students, including polyominoes, supertangrams, and polyarcs.

• Hyperbolic Planar Tessellations

  http://www.plunk.org/~hatch/HyperbolicTesselations/
  Don Hatch's page on hyperbolic tesselations with numerous illustrations.

• Lego Pentominos

  http://www.ericharshbarger.org/lego/pentominoes.html
  Eric Harshbarger. This puzzle maker says that the hard part was finding legos in enough different colors.

• Logical Art and the Art of Logic

  http://www.basic.northwestern.edu/g-buehler/pentominoes/
  Pentomino pictures, software and other resources by Guenter Albrecht-Buehler.

• Mathforum : a Pentomino Problem

  http://mathforum.org/pom/project2.95.html
  Geometry Forum: Lists the pentominoes; fold them to form a cube; play a pentomino game. (project of the month, 1995)

• Mathforum : Minimal Domino Tiling

  http://mathforum.org/wagon/spring97/p826.html
  Tiling a square without cutting it into two.(Problem of the week 826, Spring 1997)

• Mathforum : Tiling Rectangles from Ell

  http://mathforum.org/wagon/spring98/p856.html
  Stan Wagon asks which rectangles can be tiled with an ell-tromino.

• Maximum Convex Hulls of Connected Systems of Segments and of Polyominoes

  http://www.maths.soton.ac.uk/EMIS/journals/BAG/vol.35/no.1/b35h1har.abs
  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

  http://www.vicher.cz/puzzle/
  Polyforms (polyominoes, and polyiamonds) graphics, tables and resources (English/Czech).

• Packing Shapes

  http://www.stetson.edu/~efriedma/packing.html
  Erich Friedman's Introduction to a variety of packing and tiling problems.

• Pairwise Touching Hypercubes

  http://www.stetson.edu/~efriedma/mathmagic/0903.html
  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

  http://www.virtu-software.com/PentoMania/
  Pentomino based puzzle game lets children solve and create geometric puzzles. Win32 software, try or buy.

• Pentomino Applet

  http://www.cs.cmu.edu/~desilva/pento/pento.html
  Rujith de Silva's applet puzzle offers games of four different sized rectangles. Source code available. [Java]

• Pentomino HungarIQa

  http://www.pentomino.tvnet.hu/
  Kati presents a pentomino puzzle using poly-rhombs instead of poly-squares. [English/French/German/Hungarian]

• Pentomino Relationships

  http://abasmith.co.uk/pentanomes/pentanomes.html
  Symmetries in the families of rectangular solutions.

• Pentominoes

  http://www.andrews.edu/~calkins/math/pentos.htm
  Expository paper by R. Bhat and A. Fletcher. Covers pre-Golomb discoveries. the triplication problem and other aspects.

• Pentominos

  http://www.mathematische-basteleien.de/pentominos.htm
  Graphics problems, solutions (including animated GIF) and links. (English/German through main page)

• Pentominos

  http://www.mathematik.ch/anwendungenmath/pento/
  B. Berchtold's applet helps tile a 6x10 rectangle. [German]

• Pentominos Puzzle Solver

  http://math.hws.edu/xJava/PentominosSolver/
  David Eck's graphical solver applet uses recursive technique. Source code available. [Java]

• Polyform and Dissection Puzzle Links

  http://web.inter.nl.net/users/C.Eggermont/Links.new/Puzzles/Polyforms.and.dissection/index.noframe.shtml
  Christian Eggermont's link page.

• Polyform Curiosities

  http://userpages.monmouth.com/~colonel/polycur.html
  Topics include exclusion, compatibility, and wallpaper. Includes examples and charts.

• Polyforms

  http://www.mathpuzzle.com/polyom.htm
  Ed Pegg Jr.'s site has pages on tiling, packing, and related problems involving polyominos, polyiamonds, polyspheres, and related shapes.

• Polygon Puzzle

  http://freecode.com/projects/hextk
  Open source polyomino and polyform placement solitaire game.

• Polyiamond Exclusion

  http://www.monmouth.com/~colonel/xpoly/xpoly.html
  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

  http://www.polyomino.org.uk/mathematics/polyform-tiling/
  Joseph Myer's tables of polyominoes and of polyomino tilings, in Postscript format.

• Polyomino Enumeration

  http://www.mathpages.com/home/kmath039.htm
  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

  http://members.tripod.com/~modularity/pol.htm
  Describes a numerical invariant that can be used to classify polyominoes.

• Polypolygon Tilings

  http://www.uwgb.edu/dutchs/symmetry/polypoly.htm
  S. Dutch discusses polyominoes, poliamonds, and polypolygons with special attention to tiling characteristics.

• Puzzle Fun

  http://www.eldar.org/~problemi/pfun/pfun.html
  Newsletter edited by Rodolfo Kurchan about pentominoes and other math problems.

• Rectifiable Polyomino

  http://www.eklhad.net/polyomino/
  Karl Dahlke explains and demonstrates tiling. Includes C-program source.

• Schröder Triangles, Paths, and Parallelogram Polyominoes

  http://diamond.boisestate.edu/~sulanke/PAPER1/PergolaSulanke/PergolaSulanke.html
  A paper on their enumeration by Elisa Pergola and Robert A. Sulanke.

• Somatic

  http://www.moerig.com/somatic/
  A solver for arbitrary polyomino and polycube puzzles. Binary code and source downloads available.

• Sqfig and Sqtile

  http://www.lrdev.com/lr/c/sqfig.html
  Eric Laroche presents computer programs for generating polyominoes and polyomino tilings. Includes source codes in C, and binaries.

• The Geometry Junkyard: Polyominoes

  http://www.ics.uci.edu/~eppstein/junkyard/polyomino.html
  Numerous links, sorted alphabetically.

• The Mathematics of Polyominoes

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

• The Pentomino Dictionary by Gilles Esposito-Farèse

  http://www.gef.free.fr/pento.html
  English words that can be written using the pentomino name letters FILNPTUVWXYZ and other related curiosities, including a homage to Georges Perec. (English/French).

• The Poly Pages

  http://www.recmath.com/PolyPages/
  About various polyforms - polyominoes, polyiamonds, polycubes, and polyhexes.

• The Three Dimensional Polyominoes of Minimal Area

  http://www.combinatorics.org/Volume_3/Abstracts/v3i1r27.html
  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).

• Thorleif's SOMA Page

  http://www.fam-bundgaard.dk/SOMA/SOMA.HTM
  SOMA puzzle site with graphics, newsletter and software.

• Unbalanced Anisohedral Tiling

  http://www.angelfire.com/mn3/anisohedral/unbalanced.html
  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

  http://www.geom.uiuc.edu/java/tetris/
  Java applet demonstres that this tetromino-packing game is a forced win for the side dealing the tetrominoes. Complete with mathematical proof. [Java]

 

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