Top > Science > Math > Recreations > Polyominoes
Polyominoes
Listings:
  • Gamepuzzles - Polyomino and polyform games and puzzles manufactured by Kadon Enterprises Inc.
  • Some Variations on the Theme of Polyomino - Looks at patterns that illustrate how the squares of polyominos are connected to each other.
  • Polyominoes - Describes a numerical invariant that can be used to classify polyominoes.
  • Polyominoes: Theme and Variations - A brief essay with some references.
  • The Geometry Junkyard: Polyominoes - Numerous links, sorted alphabetically.
  • Polyomino and Polyhex Tiling - Joseph Myer's tables of polyominoes and of polyomino tilings, in Postscript format.
  • Steve and Susan's Puzzles - Handmade wooden Pentomino and other puzzles; books.
  • 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.
  • Miroslav Vicher's Puzzles Pages - Polyforms (polyominoes, and polyiamonds) graphics, tables and resources (English/Czech).
  • Gerard's Universal Polyomino Solver - 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
  • A Puzzle by Enrich Friedman - Every square can be dissected into L-ominoes. Can every Pythagorean square? Conjecture needs proof.
  • Pentomino Relationships - Symmetries in the families of rectangular solutions.
  • Information on Pentomino Puzzles - At the Combinatorial Object Server.
  • Pentamini pentaminos pentominoes - A container of mathematical games, gadgets and software. (English/Italian)
  • Pentomino Covers - Problems on minimal covers.
  • Hepto - Some packings of the 108 heptominoes (with unit thickness) into various blocks.
  • Tiling UROP Homepage - Undergraduate Research Project in Random Tilings.
  • Eternity Page - Alex Selby's page with a description of his solution method, with illustrations in .png and .pdf files.
  • Tiling and Packing Results of Torsten Sillke - Polyominoes, polycubes and polyspheres.
  • Solomon W. Golomb - Home Page of the inventor of polyominoes. Includes biography, black and white picture, research interests and publications list.
  • Arnab's Pentominos Puzzle - Fast Pentominos puzzle solver, works on DOS/Windows platform. Free downloads.
  • 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.
  • Pentomino, Homepage - Lorente Philippe's site describes the building blocks, nomenclature, solutions, and numerous games. (French/English)
  • Thorleif's SOMA Page - SOMA puzzle site with graphics, newsletter and software.
  • 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).
  • Schröder Triangles, Paths, and Parallelogram Polyominoes - A paper on their enumeration by Elisa Pergola and Robert A. Sulanke.
  • Pentominos - Graphics problems, solutions (including animated GIF) and links. (English/German through main page)
  • 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]
  • Logical Art and the Art of Logic - Pentomino pictures, software and other resources by Guenter Albrecht-Buehler.
  • The Soma Cube - Soma-solving program in QBASIC by Courtney McFarren.
  • Taniguchi's Programs - Windows software to solve polyiamond and sliding block puzzles.
  • Pento-Mania - Pentomino based puzzle game lets children solve and create geometric puzzles. Win32 software, try or buy.
  • R&A Media, Inc. - Manufactures wooden puzzles of polyomino type. Includes Prices, tips, hints and pages with solution counts.
  • Cynthia Lanius' Lesson: Polyominoes Introduction - From tetris to hexominoes, Cynthia explains them in color.
  • Pentomino applet - Fill up a given area using pentomino shapes, rotating and flipping them. Three levels of difficulty.[Java].
  • Java pentominoes - Thery families web site with pentomino solver. (English/French)[Java].
  • Somatic - A solver for arbitrary polyomino and polycube puzzles. Binary code and source downloads available.
  • Counting Horizontally Convex Polyominoes - Journal of Integer Sequences, Vol. 2 (1999), Article 99.1.8. Defines and counts horizontal convexity.
  • What is a Golygon? - Harry Smith describes Dr. Dewdney's article in the July 1990 Scientific American's Mathematical Recreations column.
  • Puzzle Fun - Newsletter edited by Rodolfo Kurchan about pentominoes and other math problems.
  • Blocking polyominos - Rodolfo Kurchan asks, for each k, what is the smallest polyomino such that k copies can form a blocked pattern. With solutions.
  • Canonical polygons - Ronald Kyrmse investigates grid polygons in which all side lengths are one or sqrt(2).
  • Pentominos Puzzle Solver - David Eck's graphical solver applet uses recursive technique. Source code available. [Java]
  • sqfig and sqtile - Eric Laroche presents computer programs for generating polyominoes and polyomino tilings. Includes source codes in C, and binaries.
  • Polyomino Fuzion game - Puzzles using pentominoes and hexominoes. Fuzion, game that designs and (semi-)automatically finds solutions. Links.
  • A dissection puzzle - T. Sillke asks for dissections of two heptominoes into squares.
  • The Mathematics of Polyominoes - Kevin Gong's home page includes articles, programs for Mac, Win and Java.
  • square into similar triangles - T.Sillke discusses the dissection problem.
  • my polyomino page - Michael Reid's numerous articles on polyominoes and tilnig, with references and links.
  • Equilateral pentagons - Jorge Luis Mireles Jasso investigates these polygons and dissects various polyominos into them. Animations show cases of infinite solutions.
  • Pentominoes - Expository paper by R. Bhat and A. Fletcher. Covers pre-Golomb discoveries. the triplication problem and other aspects.
  • Rectifiable polyomino - Karl Dahlke explains and demonstrates tiling. Includes C-program source.
  • Flexagons - Folded paper polyiamonds which can be unfolded to show hidden faces. Make interesting school projects.
  • Pentominoes - an introduction - Centre for Innovation in Mathematics Teaching presents colourful examples of many tiling problems, duplication, triplication, etc.
  • Packing Polyominoes - Erich Friedman's Introduction to a variety of packing and tiling problems.
  • Harold McIntosh's flexagon papers - Including copies of the original 1962 Conrad-Hartline papers. Abstract, html-pages, or .pdf documents.
  • 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.
  • Flexagons - Conrad and Hartline's 1962 article on Flexagons.
  • Gerard's Pentomino Page - Illustrates the 12 shapes. symmetrical combinations.
  • Golygons - Harry J. Smith's explains polyominoes with consecutive integer side lengths.
  • Golygons by Mathworld - What they are, and how to find them.
  • The Poly Pages - About various polyforms - polyominoes, polyiamonds, polycubes, and polyhexes. (Companion sites available in French/German/Italian, look up the respective languages under TOP:WORLD:...)
  • Polyform and dissection puzzle links - Christian Eggermont's link page.
  • Polyforms - . Ed Pegg Jr.'s site has pages on tiling, packing, and related problems involving polyominos, polyiamonds, polyspheres, and related shapes.
  • Polyform spirals - Jorge Luis Mireles explains finite and infinite spirals made up of polyforms.
  • 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.
  • Polyiamonds - Mathforum. This Geometry problem of the week asks whether a six-point star can be dissected to form eight distinct hexiamonds.
  • 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.
  • 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]
  • 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.
  • Anna's Pentomino Page - Anna Gardberg makes pentominoes out of sculpey and agate.
  • hexiamonds - George Huttlin explains and illustrates these shapes composed of 6 equilateral triangles, which in turn tiles different forms.
  • George Huttlin's Puzzle Page - George Huttlin shares some ramblings in the world of polyominoes.
  • Isoperimetric polygons - Livio Zucca tiles polygons of equal perimeter, or isoperiploes.
  • Knight's Move Tessellations - Dan Thomasson looks at tesselations with numerous unexpected shapes traced out by knight moves.
  • 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.
  • Lego Pentominos - Eric Harshbarger. This puzzle maker says that the hard part was finding legos in enough different colors.
  • Polygon Puzzle - Open source polyomino and polyform placement solitaire game.
  • The MindBlock - R & A Media presents its puzzles including a chessboard cut into twelve interlocking polyominos.
  • Polyomino applet - Wil Laan's applet searches for solution of packing hexominoes into more than 45 different shapes.[Java]
  • 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.)
  • Mathforum : minimal domino tiling - Tiling a square without cutting it into two.(Problem of the week 826, Spring 1997)
  • Tiling of Pythagorean triplets - Joe Fields suggests that L-decomposition of squares of Pythagorean triplets could always be tiled.
  • Soma cube applet - Mehta & Ward Alberg explains the soma cube and provides an applet for practice. Source codes included. [Java]
  • Animal enumerations - Enumeration on regular tilings of the Euclidean and Hyperbolic planes.
  • Tesselating locking polyominos - Bob Newman examines the history of the subject and presents his minimal solutions.
  • 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).
  • Three nice pentomino coloring problems - Alexandre Owen Muñiz presents the Icehouse set which lends itself to different polyomino coloring games.
  • Mathforum : Tiling rectangles from ell - Stan Wagon asks which rectangles can be tiled with an ell-tromino.
  • Pentominos - B. Berchtold's applet helps tile a 6x10 rectangle. [German]
  • Random domino tiling of an Aztec diamond - Matthew Blum demonstrates the properties of random domino tiling of an Aztec diamond. Interactive graphics display.
  • The Pentominoes Page - Jay Jenicek's page hosted by Puzzlecraft. Includes software for a game described on the page (2-3 players).
  • 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).
  • Pentomino Applet - Rujith de Silva's applet puzzle offers games of four different sized rectangles. [Java]
  • 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.
  • Dancing links - Don Knuth discusses implementation details of polyomino search algorithms.
  • Polyomino tiling - . Joseph Myers classifies the n-ominoes up to n=15 according to how symmetrically they can tile the plane.
  • Pentomino dissection of a square annulus - From Scott Kim's Inversions Gallery.

Google
 
Web hop2.co.uk

Help build the largest human-edited directory on the web.
Submit a Site - Open Directory Project - Become an Editor
Other sites of interest: whaddyafancy? | keithhinde.com