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  Polyominoes (96)

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Featured Websites in this category
http://www.xs4all.nl/~gp/PolyominoSolver/Polyomino.html
Featured Site Gerard's Universal Polyomino Solver Open in a new browser windowLink Details
- 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 prob
- http://www.xs4all.nl/~gp/PolyominoSolver/Polyomino.html

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Regular Websites in this category

Pentominoes : an Introduction Open in a new windowLink Details
- 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

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Eithan's Pentominoes-3D Applet Solver Open in a new windowLink Details
- Solves given Pentominoes 3D puzzles. Solution is displayed in 3-D with disassembly and rotations.[Java applet]
- http://www.panda.co.il/eithan/pento/Pentominoes3D.html

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Tiling Stuff Open in a new windowLink Details
- 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

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Random Domino Tiling of an Aztec Diamond Open in a new windowLink Details
- Matthew Blum's undergraduate project demonstrates the properties of random domino tiling of an Aztec diamond. Interactive graphics display included.
- http://www.math.wisc.edu/~propp/tiling/

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Miroslav Vicher's Puzzles Pages Open in a new windowLink Details
- Polyforms (polyominoes, and polyiamonds) graphics, tables and resources (English/Czech).
- http://www.vicher.cz/puzzle/

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Pairwise Touching Hypercubes Open in a new windowLink Details
- 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

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Hyperbolic Planar Tessellations Open in a new windowLink Details
- Don Hatch's page on hyperbolic tesselations with numerous illustrations.
- http://www.hadron.org/~hatch/HyperbolicTesselations/

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Pentomino Puzzles. Open in a new windowLink Details
- Pentomino solver with download. Windows 95 and later required. [German/English]
- http://www.exi-online.de/html/eintritt_e.html

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Tiling with Notched Cubes Open in a new windowLink Details
- 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/

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The Tiling Puzzle Games of OOG Open in a new windowLink Details
- Mr. Confetti presents a Windows and Java game for tangrams, polyominoes, and polyhexes.
- http://www.mcmprod.com/

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

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

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Primes of a 14-omino Open in a new windowLink Details
- 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

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

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A Pentominoes Project from Belgium Open in a new windowLink Details
- Secondary School project about pentominoes and fun with math. History, descriptions, and problems. Bi-monthly pentomino competition. A solver is available. [English, French, Dutch]
- http://home.scarlet.be/~demeod/

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

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The Poly Pages Open in a new windowLink Details
- About various polyforms - polyominoes, polyiamonds, polycubes, and polyhexes.
- http://www.recmath.com/PolyPages/

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Polypolygon Tilings Open in a new windowLink Details
- S. Dutch discusses polyominoes, poliamonds, and polypolygons with special attention to tiling characteristics.
- http://www.uwgb.edu/dutchs/symmetry/polypoly.htm

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Mathforum : a Pentomino Problem Open in a new windowLink Details
- 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

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Polyomino Enumeration Open in a new windowLink Details
- 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

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Pentomino Dissection of a Square Annulus Open in a new windowLink Details
- From Scott Kim's Inversions Gallery.
- http://www.scottkim.com/inversions/gallery/golomb.html

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Polyomino Tiling Open in a new windowLink Details
- Joseph Myers classifies the n-ominoes up to n=15 according to how symmetrically they can tile the plane.
- http://www.srcf.ucam.org/~jsm28/tiling/

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

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Pentomino Applet Open in a new windowLink Details
- 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

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Pentominos Open in a new windowLink Details
- B. Berchtold's applet helps tile a 6x10 rectangle. [German]
- http://www.mathematik.ch/anwendungenmath/pento/

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

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Three Nice Pentomino Coloring Problems Open in a new windowLink Details
- Alexandre Owen Muñiz presents the Icehouse set which lends itself to different polyomino coloring games.
- http://xprt.net/~munizao/mathrec/pentcol.html

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The Three Dimensional Polyominoes of Minimal Area Open in a new windowLink Details
- 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

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Tesselating Locking Polyominos Open in a new windowLink Details
- Bob Newman examines the history of the subject and presents his minimal solutions.
- http://www.noggs.dsl.pipex.com/ts/

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Animal Enumerations Open in a new windowLink Details
- Enumeration on regular tilings of the Euclidean and Hyperbolic planes.
- http://www.ieeta.pt/~tos/animals.html

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Soma Cube Applet Open in a new windowLink Details
- Mehta & Ward Alberg explains the soma cube and provides an applet for practice. Source codes included. [Java]
- http://users.ids.net/~salberg/soma/Soma.html

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

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

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Maximum Convex Hulls of Connected Systems of Segments and of Polyominoes Open in a new windowLink Details
- 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

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Polyomino Applet Open in a new windowLink Details
- Wil Laan's applet searches for solution of packing hexominoes into more than 45 different shapes.[Java]
- http://home.quicknet.nl/mw/prive/wil.laan/puzzle/cornucopia.html

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Polygon Puzzle Open in a new windowLink Details
- Open source polyomino and polyform placement solitaire game.
- http://freshmeat.net/projects/hextk/

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

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The Mathematics of Polyominoes Open in a new windowLink Details
- Kevin Gong offers download of his polyominoes games shareware for Windows and Mac. 100 boards are included. A Java version is under development.
- http://www.kevingong.com/Polyominoes/

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Knight's Move Tessellations Open in a new windowLink Details
- Dan Thomasson looks at tesselations with numerous unexpected shapes traced out by knight moves.
- http://www.borderschess.org/KTtess.htm

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Anna's Pentomino Page Open in a new windowLink Details
- Anna Gardberg makes pentominoes out of sculpey and agate.
- http://www.geom.uiuc.edu/~summer95/gardberg/pent.html

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Unbeatable Tetris Open in a new windowLink Details
- 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/

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Unfolding the Tesseract Open in a new windowLink Details
- 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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Polyiamonds Open in a new windowLink Details
- Mathforum. This Geometry problem of the week asks whether a six-point star can be dissected to form eight distinct hexiamonds.
- http://mathforum.org/pow/solutio4.html

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Polyiamond Exclusion Open in a new windowLink Details
- 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

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Polyforms Open in a new windowLink Details
- 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

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

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Golygons by Mathworld Open in a new windowLink Details
- What they are, and how to find them.
- http://mathworld.wolfram.com/Golygon.html

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Gerard's Pentomino Page Open in a new windowLink Details
- Illustrates the 12 shapes. symmetrical combinations.
- http://www.xs4all.nl/~gp/pentomino.html

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Flexagons Open in a new windowLink Details
- Conrad and Hartline's 1962 article on Flexagons.
- http://delta.cs.cinvestav.mx/~mcintosh/comun/flexagon/flexagon.html

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Six Squares Problem Open in a new windowLink Details
- 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.
- http://mathforum.org/pow/solution22.html

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

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Packing Shapes Open in a new windowLink Details
- Erich Friedman's Introduction to a variety of packing and tiling problems.
- http://www.stetson.edu/~efriedma/packing.html

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Rectifiable Polyomino Open in a new windowLink Details
- Karl Dahlke explains and demonstrates tiling. Includes C-program source.
- http://www.eklhad.net/polyomino/

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Pentominoes Open in a new windowLink Details
- 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

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My Polyomino Page Open in a new windowLink Details
- Michael Reid's numerous articles on polyominoes and tilnig, with references and links.
- http://www.math.ucf.edu/~reid/Polyomino/index.html

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Square into Similar Triangles Open in a new windowLink Details
- T.Sillke discusses the dissection problem.
- http://www.mathematik.uni-bielefeld.de/~sillke/PROBLEMS/similar.tri

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A Dissection Puzzle Open in a new windowLink Details
- T. Sillke asks for dissections of two heptominoes into squares.
- http://www.mathematik.uni-bielefeld.de/~sillke/CONTEST/h7-square

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Polyomino Fuzion Game Open in a new windowLink Details
- Puzzles using pentominoes and hexominoes. Fuzion, game that designs and (semi-)automatically finds solutions. Links.
- http://home.earthlink.net/~kenzelt/

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Sqfig and Sqtile Open in a new windowLink Details
- 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

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Pentominos Puzzle Solver Open in a new windowLink Details
- David Eck's graphical solver applet uses recursive technique. Source code available. [Java]
- http://math.hws.edu/xJava/PentominosSolver/

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

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Blocking Polyominos Open in a new windowLink Details
- Rodolfo Kurchan searchss 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

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Puzzle Fun Open in a new windowLink Details
- Newsletter edited by Rodolfo Kurchan about pentominoes and other math problems.
- http://www.eldar.org/~problemi/pfun/pfun.html

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Counting Horizontally Convex Polyominoes Open in a new windowLink Details
- 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

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Somatic Open in a new windowLink Details
- A solver for arbitrary polyomino and polycube puzzles. Binary code and source downloads available.
- http://www.moerig.com/somatic/

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

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

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Taniguchi's Programs Open in a new windowLink Details
- Windows software to solve polyiamond and sliding block puzzles.
- http://homepage2.nifty.com/yuki-tani/index_e.html

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

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Schröder Triangles, Paths, and Parallelogram Polyominoes Open in a new windowLink Details
- A paper on their enumeration by Elisa Pergola and Robert A. Sulanke.
- http://diamond.boisestate.edu/~sulanke/PAPER1/PergolaSulanke/PergolaSulanke.html

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The Pentomino Dictionary by Gilles Esposito-Farèse Open in a new windowLink Details
- 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.iap.fr/users/esposito/pento.html

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Thorleif's SOMA Page Open in a new windowLink Details
- SOMA puzzle site with graphics, newsletter and software.
- http://www.fam-bundgaard.dk/SOMA/SOMA.HTM

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Christopher Monckton's Eternity Puzzle Open in a new windowLink Details
- 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

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Solomon W. Golomb Open in a new windowLink Details
- Home Page of the inventor of polyominoes. Includes biography, black and white picture, research interests and publications list.
- http://commsci.usc.edu/faculty/golomb.html

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Tiling and Packing Results of Torsten Sillke Open in a new windowLink Details
- Polyominoes, polycubes and polyspheres.
- http://www.mathematik.uni-bielefeld.de/~sillke/results.html

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Eternity Page Open in a new windowLink Details
- 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

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Hepto Open in a new windowLink Details
- Some packings of the 108 heptominoes (with unit thickness) into various blocks.
- http://www.pisquaredoversix.force9.co.uk/Hepto.htm

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Pentomino Covers Open in a new windowLink Details
- Problems on minimal covers.
- http://www.xprt.net/~munizao/polycover/

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Information on Pentomino Puzzles Open in a new windowLink Details
- At the Combinatorial Object Server.
- http://www.theory.csc.uvic.ca/~cos/inf/misc/PentInfo.html

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Pentomino Relationships Open in a new windowLink Details
- Symmetries in the families of rectangular solutions.
- http://www.snaffles.demon.co.uk/pentanomes/pentanomes.html

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Polyomino and Polyhex Tiling Open in a new windowLink Details
- Joseph Myer's tables of polyominoes and of polyomino tilings, in Postscript format.
- http://student.cusu.cam.ac.uk/~jsm28/tiling/

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The Geometry Junkyard: Polyominoes Open in a new windowLink Details
- Numerous links, sorted alphabetically.
- http://www.ics.uci.edu/~eppstein/junkyard/polyomino.html

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Polyominoes: Theme and Variations Open in a new windowLink Details
- 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://www.cwi.nl/~jankok/etc/Polyomino.html

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Gamepuzzles Open in a new windowLink Details
- Polyomino and polyform games and puzzles manufactured by Kadon Enterprises Inc.
- http://www.gamepuzzles.com/

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