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Polypolygon tilings
S. Dutch discusses polyominoes, poliamonds, and polypolygons with special attention to tiling characteristics.
http://www.uwgb.edu/dutchs/symmetry/polypo...
Pentomino, Homepage
Lorente Philippe's site describes the building blocks, nomenclature, solutions, and numerous games. (French/English)
http://membres.lycos.fr/pentomino/index.ht...
Somatic
A solver for arbitrary polyomino and polycube puzzles. Binary code and source downloads available.
http://www.moerig.com/somatic/
Taniguchi's Programs
Windows software to solve polyiamond and sliding block puzzles.
http://homepage2.nifty.com/yuki-tani/index...
A dissection puzzle
T. Sillke asks for dissections of two heptominoes into squares.
http://www.mathematik.uni-bielefeld.de/~si...
Puzzle Fun
Newsletter edited by Rodolfo Kurchan about pentominoes and other math problems.
http://www.eldar.org/~problemi/pfun/pfun.h...
The Mathematics of Polyominoes
Kevin Gong's home page includes articles, programs for Mac, Win and Java.
http://kevingong.com/Polyominoes/Math.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/
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/pento...
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/Not...
Animal enumerations
Enumeration on regular tilings of the Euclidean and Hyperbolic planes.
http://www.ieeta.pt/~tos/animals.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/old...
Knight's Move Tessellations
Dan Thomasson looks at tesselations with numerous unexpected shapes traced out by knight moves.
http://www.borderschess.org/KTtess.htm
Pentomino Relationships
Symmetries in the families of rectangular solutions.
http://www.snaffles.demon.co.uk/pentanomes...
Rectifiable polyomino
Karl Dahlke explains and demonstrates tiling. Includes C-program source.
http://www.eklhad.net/polyomino/index.html
Schröder Triangles, Paths, and Parallelogram Polyominoes
A paper on their enumeration by Elisa Pergola and Robert A. Sulanke.
http://diamond.boisestate.edu/~sulanke/PAP...
Pentominos Puzzle Solver
David Eck's graphical solver applet uses recursive technique. Source code available. [Java]
http://math.hws.edu/xJava/PentominosSolver...
The tiling puzzle games of OOG
Mr. Confetti presents a Windows and Java game for tangrams, polyominoes, and polyhexes.
http://www.mcmprod.com/
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
Java pentominoes
Thery families web site with pentomino solver. (English/French)[Java].
http://www.thery.free.fr/index.php?option=...
Polyominoes
Describes a numerical invariant that can be used to classify polyominoes.
http://members.tripod.com/~modularity/pol....
Livio Zucca's polyomino-covered cube
Colorful illustrations demonstrate how closed surfaces could be covered by polyominoes.
http://www.geocities.com/liviozuc/pag3_eng...
The Geometry Junkyard: Polyominoes
Numerous links, sorted alphabetically.
http://www.ics.uci.edu/~eppstein/junkyard/...
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/...
Polygon Puzzle
Open source polyomino and polyform placement solitaire game.
http://freshmeat.net/projects/hextk/
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/...
square into similar triangles
T.Sillke discusses the dissection problem.
http://www.mathematik.uni-bielefeld.de/~si...
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...
Pento
Amamas Software offers a pentomino solving software.
http://ourworld.compuserve.com/homepages/D...
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.h...
Golygons by Mathworld
What they are, and how to find them.
http://mathworld.wolfram.com/Golygon.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
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/Abst...
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/
Logical Art and the Art of Logic
Pentomino pictures, software and other resources by Guenter Albrecht-Buehler.
http://www.basic.northwestern.edu/g-buehle...
Pentomino dissection of a square annulus
From Scott Kim's Inversions Gallery.
http://www.scottkim.com/inversions/gallery...
Isoperimetric polygons
Livio Zucca tiles polygons of equal perimeter, or isoperiploes.
http://www.geocities.com/liviozuc/polyedge...
Pentomino Applet
Rujith de Silva's applet puzzle offers games of four different sized rectangles. [Java]
http://www.cs.cmu.edu/~desilva/pento/pento...
Polyominoes: Theme and Variations
A brief essay with some references.
http://www.cwi.nl/~jankok/etc/Polyomino.ht...
Polyform and dissection puzzle links
Christian Eggermont's link page.
http://web.inter.nl.net/users/C.Eggermont/...
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/Hal...
Blocking polyominos
Rodolfo Kurchan asks, for each k, what is the smallest polyomino such that k copies can form a blocked pattern. With solutions.
http://www.eldar.org/~problemi/pfun/blocke...
Polyomino Fuzion game
Puzzles using pentominoes and hexominoes. Fuzion, game that designs and (semi-)automatically finds solutions. Links.
http://home.earthlink.net/~kenzelt/
Anna's Pentomino Page
Anna Gardberg makes pentominoes out of sculpey and agate.
http://www.geom.uiuc.edu/~summer95/gardber...
Polyomino tiling
. 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/
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/14...
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/p...
Tiling and Packing Results of Torsten Sillke
Polyominoes, polycubes and polyspheres.
http://www.mathematik.uni-bielefeld.de/~si...
Pentomino
Puzzels oplossen, meedoen met prijsvragen voor wiskunde liefhebbers. De site is Nederlands-, Engels- en Franstalig.
http://home.scarlet.be/~demeod/
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
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....
Soma cube applet
Mehta & Ward Alberg explains the soma cube and provides an applet for practice. Source codes included. [Java]
http://users.ids.net/~salberg/soma/Soma.ht...
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
George Huttlin's Puzzle Page
George Huttlin shares some ramblings in the world of polyominoes.
http://members.aol.com/huttlin/pentominoes...
Polyomino and Polyhex Tiling
Joseph Myer's tables of polyominoes and of polyomino tilings, in Postscript format.
http://student.cusu.cam.ac.uk/~jsm28/tilin...
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
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.h...
Polyform spirals
Jorge Luis Mireles explains finite and infinite spirals made up of polyforms.
http://www.geocities.com/jorgeluismireles/...
Tiling UROP Homepage
Undergraduate Research Project in Random Tilings.
http://www.math.wisc.edu/~propp/tiling/
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/Eig...
Cynthia Lanius' Lesson: Polyominoes Introduction
From tetris to hexominoes, Cynthia explains them in color.
http://math.rice.edu/~lanius/Lessons/Polys...
Hyperbolic planar tessellations
Don Hatch's page on hyperbolic tesselations with numerous illustrations.
http://www.hadron.org/~hatch/HyperbolicTes...
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/pu...
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://www.iap.fr/users/esposito/pento.htm...
Arnab's Pentominos Puzzle
Fast Pentominos puzzle solver, works on DOS/Windows platform. Free downloads.
http://www.geocities.com/hirak_99/goodies/...
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
Thorleif's SOMA Page
SOMA puzzle site with graphics, newsletter and software.
http://www.fam-bundgaard.dk/SOMA/SOMA.HTM
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...
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 in the works.
http://www.kevingong.com/Polyominoes/
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
Dancing links
Don Knuth discusses implementation details of polyomino search algorithms.
http://www-cs-faculty.stanford.edu/~knuth/...
Pentominos
B. Berchtold's applet helps tile a 6x10 rectangle. [German]
http://www.mathematik.ch/anwendungenmath/p...
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...
Erich's Packing Center
Graphics and links for various packing, tiling and covering problems.
http://www.stetson.edu/~efriedma/packing.h...
Hepto
Some packings of the 108 heptominoes (with unit thickness) into various blocks.
http://www.pisquaredoversix.force9.co.uk/H...
The Poly Pages
About various polyforms - polyominoes, polyiamonds, polycubes, and polyhexes.
http://www.recmath.com/PolyPages/
Golygons
Harry J. Smith's explains polyominoes with consecutive integer side lengths.
http://www.geocities.com/hjsmithh/Golygons...
Pentominos
Graphics problems, solutions (including animated GIF) and links. (English/German through main page)
http://www.mathematische-basteleien.de/pen...
Random domino tiling of an Aztec diamond
Matthew Blum demonstrates the properties of random domino tiling of an Aztec diamond. Interactive graphics display.
http://www.math.wisc.edu/~propp/tiling/www...
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/xpo...
Pento-Mania
Pentomino based puzzle game lets children solve and create geometric puzzles. Win32 software, try or buy.
http://www.virtu-software.com/PentoMania/
Pentomino HungarIQa
Kati presents a pentomino puzzle using poly-rhombs instead of poly-squares. [English/French/German/Hungarian]
http://www.pentomino.tvnet.hu/
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/
A Puzzle by Enrich Friedman
Every square can be dissected into L-ominoes. Can every Pythagorean square? Conjecture needs proof.
http://www.math.uic.edu/~fields/puzzle/puz...
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....
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/u...
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/...
Lego Pentominos
Eric Harshbarger. This puzzle maker says that the hard part was finding legos in enough different colors.
http://www.ericharshbarger.org/lego/pentom...
Pentomino Covers
Problems on minimal covers.
http://www.xprt.net/~munizao/polycover/
Pentominopuzzles.
Pentomino solver with download. Windows 95 and later required. [German/English]
http://www.exi-online.de/html/eintritt_e.h...
Gerard's Pentomino Page
Illustrates the 12 shapes. symmetrical combinations.
http://www.xs4all.nl/~gp/pentomino.html
Miroslav Vicher's Puzzles Pages
Polyforms (polyominoes, and polyiamonds) graphics, tables and resources (English/Czech).
http://alpha.ujep.cz/~vicher/puzzle/
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/i...
Mathforum : Tiling rectangles from ell
Stan Wagon asks which rectangles can be tiled with an ell-tromino.
http://mathforum.org/wagon/spring98/p856.h...
Mathforum : a pentomino problem
from the 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
my polyomino page
Michael Reid's numerous articles on polyominoes and tilnig, with references and links.
http://www.math.ucf.edu/~reid/Polyomino/in...
Polyominoes
Introduction to Tetrominoes, Pentominoes, Hexominoes, Heptominoes, Octominoes, Fixed (translation only) Polyominoes. Numerous Links.
http://www.geocities.com/alclarke0/PolyPag...
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...
Flexagons
Conrad and Hartline's 1962 article on Flexagons.
http://delta.cs.cinvestav.mx/~mcintosh/com...
Kadon Enterprises
Creators and producers of over 80 abstract strategy games and geometric puzzles since 1980.
http://www.gamepuzzles.com/
Tesselating locking polyominos
Bob Newman examines the history of the subject and presents his minimal solutions.
http://www.noggs.dsl.pipex.com/ts/index.ht...
Polyomino problems and variations of a theme
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/Polyom...
Information on Pentomino Puzzles
At the Combinatorial Object Server.
http://www.theory.csc.uvic.ca/~cos/inf/mis...
Packing Ferrers Shapes
Alon, Bóna, and Spencer show that one can't cover very much of an n by p(n) rectangle with staircase polyominoes (where p(n) is the number of these shapes).
http://arxiv.org/PS_cache/math/pdf/9812/98...
Eithan's Pentominoes-3D Applet Solver
Solves given Pentominoes 3D puzzles. Solution is displayed in 3-D with disassembly and rotations. General information and data. [requires Java]
http://www.panda.co.il/eithan/pento/Pentom...
Pentominoes - an introduction
Centre for Innovation in Mathematics Teaching presents colourful examples of many tiling problems, duplication, triplication, etc.
http://www.ex.ac.uk/cimt/puzzles/pentoes/p...
Flexagons
Folded paper polyiamonds which can be unfolded to show hidden faces. Make interesting school projects.
http://www.enarsson.nu/Flexagon/index.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
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/...
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/HI...
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
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2006