GoSearchFor Web Directory : Science : Math : Recreations : Polyominoes

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

» Gerard's Universal Polyomino Solver Editor's Pick

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

Sites:

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

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

http://www.eldar.org/~problemi/pfun/blocked.html

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

http://sti.br.inter.net/rkyrmse/canonic-e.htm

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

» 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.
http://mathpuzzle.com/eternity.html

http://www.cs.uwaterloo.ca/journals/JIS/HICK2/chcp.html

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

$http://math.rice.edu/~lanius/Lessons/Polys/poly1.html$

» Cynthia Lanius' Lesson: Polyominoes Introduction
From tetris to hexominoes, Cynthia explains them in color.
http://math.rice.edu/~lanius/Lessons/Polys/poly1.html

http://www-cs-faculty.stanford.edu/~knuth/papers/dancing-color.ps.gz

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

http://www.archduke.demon.co.uk/eternity/index.html

» Eternity Page
Alex Selby's page with a description of his solution method, with illustrations in .png and .pdf files.
http://www.archduke.demon.co.uk/eternity/index.html

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

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

» Gerard's Pentomino Page
Illustrates the 12 shapes. symmetrical combinations.
http://www.xs4all.nl/~gp/pentomino.html

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

http://delta.cs.cinvestav.mx/~mcintosh/oldweb/pflexagon.html

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

$http://www.picciotto.org/math-ed/puzzles/$

» Henri Picciotto's Geometric Puzzles in the Classroom
Polyform puzzle lessons for math educators to use with their students, including polyominoes, supertangrams, and polyarcs.
http://www.picciotto.org/math-ed/puzzles/

http://www.plunk.org/~hatch/HyperbolicTesselations/

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

» Information on Pentomino Puzzles
At the Combinatorial Object Server.
http://www.theory.csc.uvic.ca/~cos/inf/misc/PentInfo.html

http://www.thery.free.fr/index.php?option=com_content&task=view&id=18&Itemid=44

» Java pentominoes
Thery families web site with pentomino solver. (English/French)[Java].
http://www.thery.free.fr/index.php?option=com_content&task=view&id=18&Itemid=44

» Knight's Move Tessellations
Dan Thomasson looks at tesselations with numerous unexpected shapes traced out by knight moves.
http://www.borderschess.org/KTtess.htm

http://www.ericharshbarger.org/lego/pentominoes.html

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

http://www.basic.northwestern.edu/g-buehler/pentominoes/

» Logical Art and the Art of Logic
Pentomino pictures, software and other resources by Guenter Albrecht-Buehler.
http://www.basic.northwestern.edu/g-buehler/pentominoes/

http://mathforum.org/wagon/spring97/p826.html

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

http://mathforum.org/wagon/spring98/p856.html

» Mathforum : Tiling Rectangles from Ell
Stan Wagon asks which rectangles can be tiled with an ell-tromino.
http://mathforum.org/wagon/spring98/p856.html

http://mathforum.org/pom/project2.95.html

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

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

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

» Miroslav Vicher's Puzzles Pages
Polyforms (polyominoes, and polyiamonds) graphics, tables and resources (English/Czech).
http://www.vicher.cz/puzzle/

$http://www.math.ucf.edu/~reid/Polyomino/index.html$

» My Polyomino Page
Michael Reid's numerous articles on polyominoes and tilnig, with references and links.
http://www.math.ucf.edu/~reid/Polyomino/index.html

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

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

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

http://www.virtu-software.com/PentoMania/

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

http://www.cs.cmu.edu/~desilva/pento/pento.html

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

» Pentomino Covers
Problems on minimal covers.
http://www.xprt.net/~munizao/polycover/

» Pentomino Dissection of a Square Annulus
From Scott Kim's Inversions Gallery.
http://www.scottkim.com/inversions/gallery/golomb.html

http://membres.lycos.fr/pentomino/index.html

» Pentomino Homepage
Lorente Philippe's site describes the building blocks, nomenclature, solutions, and numerous games. (French/English)
http://membres.lycos.fr/pentomino/index.html

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

» Pentomino Puzzles.
Pentomino solver with download. Windows 95 and later required. [German/English]
http://www.exi-online.de/html/eintritt_e.html

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

$http://www.andrews.edu/~calkins/math/pentos.htm$

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

http://www.cimt.plymouth.ac.uk/resources/puzzles/pentoes/pentoint.htm

» Pentominoes : an Introduction
Centre for Innovation in Mathematics Teaching presents colourful examples of many tiling problems, duplication, triplication, etc.
http://www.cimt.plymouth.ac.uk/resources/puzzles/pentoes/pentoint.htm

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

$http://math.hws.edu/xJava/PentominosSolver/$

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

http://userpages.monmouth.com/~colonel/polycur.html

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

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

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

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

» Polygon Puzzle
Open source polyomino and polyform placement solitaire game.
http://freshmeat.net/projects/hextk/

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

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

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

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

» Polyomino and Polyhex Tiling
Joseph Myer's tables of polyominoes and of polyomino tilings, in Postscript format.
http://www.srcf.ucam.org/~jsm28/tiling/

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

http://homepages.cwi.nl/~jankok/etc/Polyomino.html

» 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.
http://homepages.cwi.nl/~jankok/etc/Polyomino.html

http://www.uwgb.edu/dutchs/symmetry/polypoly.htm

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

$http://www.math.ucf.edu/~reid/Polyomino/14omino02_rect.html$

» 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.
http://www.math.ucf.edu/~reid/Polyomino/14omino02_rect.html

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

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

http://diamond.boisestate.edu/~sulanke/PAPER1/PergolaSulanke/PergolaSulanke.html

» SchrÃ¶der Triangles, Paths, and Parallelogram Polyominoes
A paper on their enumeration by Elisa Pergola and Robert A. Sulanke.
http://diamond.boisestate.edu/~sulanke/PAPER1/PergolaSulanke/PergolaSulanke.html

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

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

» Taniguchi's Programs
Windows software to solve polyiamond and sliding block puzzles.
http://homepage2.nifty.com/yuki-tani/index_e.html

» The Geometry Junkyard: Polyominoes
Numerous links, sorted alphabetically.
http://www.ics.uci.edu/~eppstein/junkyard/polyomino.html

» 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.
http://kevingong.com/Polyominoes/

» The Pentomino Dictionary by Gilles Esposito-FarÃ¨se
English words that can be written using the pentomino name letters FILNPTUVWXYZ and other related curiosities, including a homage to Georges Perec. (English/French).
http://www.gef.free.fr/pento.html

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

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

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

» Thorleif's SOMA Page
SOMA puzzle site with graphics, newsletter and software.
http://www.fam-bundgaard.dk/SOMA/SOMA.HTM

http://xprt.net/~munizao/mathrec/pentcol.html

» Three Nice Pentomino Coloring Problems
Alexandre Owen MuÃ±iz presents the Icehouse set which lends itself to different polyomino coloring games.
http://xprt.net/~munizao/mathrec/pentcol.html

$http://www.math.ucf.edu/~reid/Research/Halfstrip/$

» Tiling Rectangles and Half Strips with Congruent Polyominoes
Michael Reid's abstract of paper in the "Journal of Combinatorial Theory, Series A".
http://www.math.ucf.edu/~reid/Research/Halfstrip/

$http://www.math.ufl.edu/~squash/tilingstuff.html$

» 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.
http://www.math.ufl.edu/~squash/tilingstuff.html

$http://www.math.ucf.edu/~reid/Research/Eight/$

» Tiling a Square With Eight Congruent Polyominoes
Michael Reid's abstract of a paper in the "Journal of Combinatorial Theory, Series A".
http://www.math.ucf.edu/~reid/Research/Eight/

$http://www2.math.uic.edu/~fields/puzzle/puzzle.html$

» Tiling of Pythagorean Triplets
Joe Fields suggests that L-decomposition of squares of Pythagorean triplets could always be tiled.
http://www2.math.uic.edu/~fields/puzzle/puzzle.html

$http://www.math.ucf.edu/~reid/Research/Notched/$

» 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".
http://www.math.ucf.edu/~reid/Research/Notched/

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

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

» 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]
http://www.geom.uiuc.edu/java/tetris/

http://www.apperceptual.com/tesseract.html

» 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.
http://www.apperceptual.com/tesseract.html

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