Home > Science > Math > Recreations > Polyominoes
http://www.ieeta.pt/~tos/animals.html
Enumeration on regular tilings of the Euclidean and Hyperbolic planes.
http://www.geom.uiuc.edu/~summer95/gardberg/pent.html
Anna Gardberg makes pentominoes out of sculpey and agate.
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.
http://sti.br.inter.net/rkyrmse/canonic-e.htm
Ronald Kyrmse investigates grid polygons in which all side lengths are one or sqrt(2).
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.
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.
http://math.rice.edu/~lanius/Lessons/Polys/poly1.html
From tetris to hexominoes, Cynthia explains them in color.
http://www-cs-faculty.stanford.edu/~knuth/papers/dancing-color.ps.gz
Don Knuth discusses implementation details of polyomino search algorithms (compressed PostScript format).
http://delta.cs.cinvestav.mx/~mcintosh/comun/flexagon/flexagon.html
Conrad and Hartline's 1962 article on Flexagons.
http://www.gamepuzzles.com/
Polyomino and polyform games and puzzles manufactured by Kadon Enterprises Inc.
http://www.xs4all.nl/~gp/pentomino.html
Illustrates the 12 shapes. symmetrical combinations.
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].
http://mathworld.wolfram.com/Golygon.html
What they are, and how to find them.
http://delta.cs.cinvestav.mx/~mcintosh/oldweb/pflexagon.html
Including copies of the original 1962 Conrad-Hartline papers. Abstract, html-pages, or .pdf documents.
http://www.mathedpage.org/puzzles/
Polyform puzzle lessons for math educators to use with their students, including polyominoes, supertangrams, and polyarcs.
http://www.plunk.org/~hatch/HyperbolicTesselations/
Don Hatch's page on hyperbolic tesselations with numerous illustrations.
http://www.ericharshbarger.org/lego/pentominoes.html
Eric Harshbarger. This puzzle maker says that the hard part was finding legos in enough different colors.
http://www.basic.northwestern.edu/g-buehler/pentominoes/
Pentomino pictures, software and other resources by Guenter Albrecht-Buehler.
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)
http://mathforum.org/wagon/spring97/p826.html
Tiling a square without cutting it into two.(Problem of the week 826, Spring 1997)
http://mathforum.org/wagon/spring98/p856.html
Stan Wagon asks which rectangles can be tiled with an ell-tromino.
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.)
http://www.vicher.cz/puzzle/
Polyforms (polyominoes, and polyiamonds) graphics, tables and resources (English/Czech).
http://www.stetson.edu/~efriedma/packing.html
Erich Friedman's Introduction to a variety of packing and tiling problems.
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.
http://www.virtu-software.com/PentoMania/
Pentomino based puzzle game lets children solve and create geometric puzzles. Win32 software, try or buy.
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]
http://www.pentomino.tvnet.hu/
Kati presents a pentomino puzzle using poly-rhombs instead of poly-squares. [English/French/German/Hungarian]
http://abasmith.co.uk/pentanomes/pentanomes.html
Symmetries in the families of rectangular solutions.
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.
http://www.mathematische-basteleien.de/pentominos.htm
Graphics problems, solutions (including animated GIF) and links. (English/German through main page)
http://www.mathematik.ch/anwendungenmath/pento/
B. Berchtold's applet helps tile a 6x10 rectangle. [German]
http://math.hws.edu/xJava/PentominosSolver/
David Eck's graphical solver applet uses recursive technique. Source code available. [Java]
http://web.inter.nl.net/users/C.Eggermont/Links.new/Puzzles/Polyforms.and.dissection/index.noframe.shtml
Christian Eggermont's link page.
http://userpages.monmouth.com/~colonel/polycur.html
Topics include exclusion, compatibility, and wallpaper. Includes examples and charts.
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.
http://freecode.com/projects/hextk
Open source polyomino and polyform placement solitaire game.
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.
http://www.polyomino.org.uk/mathematics/polyform-tiling/
Joseph Myer's tables of polyominoes and of polyomino tilings, in Postscript format.
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.
http://members.tripod.com/~modularity/pol.htm
Describes a numerical invariant that can be used to classify polyominoes.
http://www.uwgb.edu/dutchs/symmetry/polypoly.htm
S. Dutch discusses polyominoes, poliamonds, and polypolygons with special attention to tiling characteristics.
http://www.eldar.org/~problemi/pfun/pfun.html
Newsletter edited by Rodolfo Kurchan about pentominoes and other math problems.
http://www.eklhad.net/polyomino/
Karl Dahlke explains and demonstrates tiling. Includes C-program source.
http://diamond.boisestate.edu/~sulanke/PAPER1/PergolaSulanke/PergolaSulanke.html
A paper on their enumeration by Elisa Pergola and Robert A. Sulanke.
http://www.moerig.com/somatic/
A solver for arbitrary polyomino and polycube puzzles. Binary code and source downloads available.
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.
http://www.ics.uci.edu/~eppstein/junkyard/polyomino.html
Numerous links, sorted alphabetically.
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.
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).
http://www.recmath.com/PolyPages/
About various polyforms - polyominoes, polyiamonds, polycubes, and polyhexes.
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).
http://www.fam-bundgaard.dk/SOMA/SOMA.HTM
SOMA puzzle site with graphics, newsletter and software.
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.
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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