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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 Pentomino Covers -
Problems on minimal covers.
http://www.xprt.net/~munizao/polycover/ Polyiamonds -
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 The Geometry Junkyard: Polyominoes -
Numerous links, sorted alphabetically.
http://www.ics.uci.edu/~eppstein/junkyard/polyomino.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 Polygon Puzzle -
Open source polyomino and polyform placement solitaire game.
http://freshmeat.net/projects/hextk/ 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 Polyomino and Polyhex Tiling -
Joseph Myer's tables of polyominoes and of polyomino tilings, in Postscript format.
http://www.srcf.ucam.org/~jsm28/tiling/ Pentominos -
B. Berchtold's applet helps tile a 6x10 rectangle. [German]
http://www.mathematik.ch/anwendungenmath/pento/ 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 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 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/ 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 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 Information on Pentomino Puzzles -
At the Combinatorial Object Server.
http://www.theory.csc.uvic.ca/~cos/inf/misc/PentInfo.html Three Nice Pentomino Coloring Problems -
Alexandre Owen Muñiz presents the Icehouse set which lends itself to different polyomino coloring games.
http://xprt.net/~munizao/mathrec/pentcol.html Polyomino Applet -
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 Rectifiable Polyomino -
Karl Dahlke explains and demonstrates tiling. Includes C-program source.
http://www.eklhad.net/polyomino/ Golygons -
Harry J. Smith's explains polyominoes with consecutive integer side lengths.
http://www.geocities.com/hjsmithh/Golygons/ 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 Livio Zucca's polyomino-covered cube -
Colorful illustrations demonstrate how closed surfaces could be covered by polyominoes.
http://www.geocities.com/liviozuc/pag3_eng.html Blocking Polyominos -
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 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://www.kevingong.com/Polyominoes/ 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 Taniguchi's Programs -
Windows software to solve polyiamond and sliding block puzzles.
http://homepage2.nifty.com/yuki-tani/index_e.html Anna's Pentomino Page -
Anna Gardberg makes pentominoes out of sculpey and agate.
http://www.geom.uiuc.edu/~summer95/gardberg/pent.html Miroslav Vicher's Puzzles Pages -
Polyforms (polyominoes, and polyiamonds) graphics, tables and resources (English/Czech).
http://www.vicher.cz/puzzle/ 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 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/ Isoperimetric Polygons -
Livio Zucca tiles polygons of equal perimeter, or isoperiploes.
http://www.geocities.com/liviozuc/polyedges.html The Tiling Puzzle Games of OOG -
Mr. Confetti presents a Windows and Java game for tangrams, polyominoes, and polyhexes.
http://www.mcmprod.com/ 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 Mathforum : Tiling Rectangles from Ell -
Stan Wagon asks which rectangles can be tiled with an ell-tromino.
http://mathforum.org/wagon/spring98/p856.html 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/ Animal Enumerations -
Enumeration on regular tilings of the Euclidean and Hyperbolic planes.
http://www.ieeta.pt/~tos/animals.html What is a Golygon? -
Harry Smith describes Dr. Dewdney's article in the July 1990 Scientific American's Mathematical Recreations column.
http://www.geocities.com/hjsmithh/Golygons/GolyWhat.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 Schröder 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 Knight's Move Tessellations -
Dan Thomasson looks at tesselations with numerous unexpected shapes traced out by knight moves.
http://www.borderschess.org/KTtess.htm 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 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 Pento -
Amamas Software offers a pentomino solving software.
http://ourworld.compuserve.com/homepages/DavidandPenny/Pento.htm Golygons by Mathworld -
What they are, and how to find them.
http://mathworld.wolfram.com/Golygon.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 Six Squares Problem -
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 Polyominoes -
Introduction to Tetrominoes, Pentominoes, Hexominoes, Heptominoes, Octominoes, Fixed (translation only) Polyominoes. Numerous Links.
http://www.geocities.com/alclarke0/PolyPages/Polyominoes.html Somatic -
A solver for arbitrary polyomino and polycube puzzles. Binary code and source downloads available.
http://www.moerig.com/somatic/ 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 Gamepuzzles -
Polyomino and polyform games and puzzles manufactured by Kadon Enterprises Inc.
http://www.gamepuzzles.com/ 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 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 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 Tesselating Locking Polyominos -
Bob Newman examines the history of the subject and presents his minimal solutions.
http://www.noggs.dsl.pipex.com/ts/ Hexiamonds -
George Huttlin explains and illustrates these shapes composed of 6 equilateral triangles, which in turn tiles different forms.
http://members.aol.com/huttlin/hexiamonds.html Arnab's Pentominos Puzzle -
Fast Pentominos puzzle solver, works on DOS/Windows platform. Free downloads.
http://www.geocities.com/hirak_99/goodies/pento.html The Poly Pages -
About various polyforms - polyominoes, polyiamonds, polycubes, and polyhexes.
http://www.recmath.com/PolyPages/ 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 Packing Polyominoes -
Mark Michell investigates packing pentominoes into rectangles of various non-integer aspect ratios in order to obtain the largest possible pieces using straight cuts.
http://www.users.bigpond.com/themichells/packing_pentominoes.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 Polyomino Fuzion Game -
Puzzles using pentominoes and hexominoes. Fuzion, game that designs and (semi-)automatically finds solutions. Links.
http://home.earthlink.net/~kenzelt/ 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 Cynthia Lanius' Lesson: Polyominoes Introduction -
From tetris to hexominoes, Cynthia explains them in color.
http://math.rice.edu/~lanius/Lessons/Polys/poly1.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 Pento-Mania -
Pentomino based puzzle game lets children solve and create geometric puzzles. Win32 software, try or buy.
http://www.virtu-software.com/PentoMania/ Polyominoes -
Describes a numerical invariant that can be used to classify polyominoes.
http://members.tripod.com/~modularity/pol.htm 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/ Thorleif's SOMA Page -
SOMA puzzle site with graphics, newsletter and software.
http://www.fam-bundgaard.dk/SOMA/SOMA.HTM Pentomino HungarIQa -
Kati presents a pentomino puzzle using poly-rhombs instead of poly-squares. [English/French/German/Hungarian]
http://www.pentomino.tvnet.hu/ Polyominoids -
Jorge Luis Mireles Jasso presents connected sets of squares in a 3d cubical lattice. Includes a Java applet as well as non-animated description.
http://www.geocities.com/jorgeluismireles/polyominoids/ Pentomino Puzzles. -
Pentomino solver with download. Windows 95 and later required. [German/English]
http://www.exi-online.de/html/eintritt_e.html 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 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 Equilateral Pentagons -
Jorge Luis Mireles Jasso investigates these polygons and dissects various polyominos into them. Animations show cases of infinite solutions.
http://www.geocities.com/jorgeluismireles/equilaterals/ Pentomino Homepage -
Lorente Philippe's site describes the building blocks, nomenclature, solutions, and numerous games. (French/English)
http://membres.lycos.fr/pentomino/index.html Pentominos -
Graphics problems, solutions (including animated GIF) and links. (English/German through main page)
http://www.mathematische-basteleien.de/pentominos.htm Xominoes -
Livio Zucca finds a set of markings for the edges of a square that lead to exactly 100 possible tiles, and asks how to fit them into a 10x10 grid.
http://www.geocities.com/liviozuc/xominoes.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 George Huttlin's Puzzle Page -
George Huttlin shares some ramblings in the world of polyominoes.
http://members.aol.com/huttlin/pentominoes.html 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 Pentomino Dissection of a Square Annulus -
From Scott Kim's Inversions Gallery.
http://www.scottkim.com/inversions/gallery/golomb.html Polypolygon Tilings -
S. Dutch discusses polyominoes, poliamonds, and polypolygons with special attention to tiling characteristics.
http://www.uwgb.edu/dutchs/symmetry/polypoly.htm Packing Shapes -
Erich Friedman's Introduction to a variety of packing and tiling problems.
http://www.stetson.edu/~efriedma/packing.html Pentominos Puzzle Solver -
David Eck's graphical solver applet uses recursive technique. Source code available. [Java]
http://math.hws.edu/xJava/PentominosSolver/ Solomon W. Golomb -
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 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/ Pentamini Pentaminos Pentominoes -
A container of mathematical games, gadgets and software. (English/Italian)
http://www.geocities.com/liviozuc/ The Soma Cube -
Soma-solving program in QBASIC by Courtney McFarren.
http://www.geocities.com/abcmcfarren/soma/soma.htm Pentomino Applet -
Fill up a given area using pentomino shapes, rotating and flipping them. Three levels of difficulty.[Java].
http://www.fwend.com/pentomino.htm Puzzle Fun -
Newsletter edited by Rodolfo Kurchan about pentominoes and other math problems.
http://www.eldar.org/~problemi/pfun/pfun.html 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/ 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 Gerard's Pentomino Page -
Illustrates the 12 shapes. symmetrical combinations.
http://www.xs4all.nl/~gp/pentomino.html Flexagons -
Conrad and Hartline's 1962 article on Flexagons.
http://delta.cs.cinvestav.mx/~mcintosh/comun/flexagon/flexagon.html 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).
http://www2.iap.fr/users/esposito/pento.html Polyform Spirals -
Jorge Luis Mireles explains finite and infinite spirals made up of polyforms.
http://www.geocities.com/jorgeluismireles/spirals/
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