Polyominoes Recreations Math

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.

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Polyominoes


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

• Logical Art and the Art of Logic - Pentomino pictures, software and other resources by Guenter Albrecht-Buehler.
• Harold McIntosh's Flexagon Papers - Including copies of the original 1962 Conrad-Hartline papers. Abstract, recreations html-pages, or .pdf documents.
• Polyominoes: Theme and Variations - Jankok presents information about filling rectangles, other polygons, recreations boxes, etc., math with dominoes, trominoes, tetrominoes, pentominoes, solid recreations pentominoes, hexiamonds, and whatever math else people have invented recreations as variations of a theme. References math included.
• Arnab's Pentominos Puzzle - Fast Pentominos puzzle solver, works on DOS/Windows platform. Free math downloads.
• Blocking Polyominos - Rodolfo Kurchan searches the smallest polyomino such that recreations a particular recreations number of copies can form a recreations blocked pattern. With recreations solutions.
• Pentomino Applet - Rujith de Silva\\'s applet puzzle offers games of recreations four different sized rectangles. Source code available. recreations [Java]
• Unfolding the Tesseract - Peter Turney lists the 261 polycubes that can be folded math in four dimensions to form the surface of a hypercube, math and provides animations of the unfolding process.
• Counting Horizontally Convex Polyominoes - Journal of Integer Sequences, Vol. 2 polyominoes polyominoes polyominoes (1999), Article 99.1.8. polyominoes Defines and counts horizontal convexity.
• Polyform Spirals - Jorge Luis Mireles explains finite and infinite spirals made up recreations of polyforms.
• Miroslav Vicher's Puzzles Pages - Polyforms (polyominoes, and polyiamonds) graphics, tables and resources (English/Czech).
• Golygons by Mathworld - What they are, and how to find them.
• Unbalanced Anisohedral Tiling - Joseph Myers and John Berglund found a polyhex math that must recreations be placed in two different ways math in a tiling of recreations a plane, such that math one placement occurs twice as often recreations as the math other.
• Three Nice Pentomino Coloring Problems - Alexandre Owen Muñiz presents the Icehouse set which polyominoes lends itself recreations to different polyomino coloring games.
• Knight's Move Tessellations - Dan Thomasson looks at tesselations with numerous unexpected math shapes traced out by knight moves.
• The Tiling Puzzle Games of OOG - Mr. Confetti presents a Windows and Java game recreations for tangrams, math polyominoes, and polyhexes.
• Pento-Mania - Pentomino based puzzle game lets children solve and recreations create geometric math puzzles. Win32 software, try or recreations buy.
• Lego Pentominos - Eric Harshbarger. This puzzle maker says that the math hard part polyominoes was finding legos in enough different math colors.
• Pentamini Pentaminos Pentominoes - A container of mathematical games, gadgets and software. (English/Italian)
• Pentominos - B. Berchtold\'s applet helps tile a 6x10 rectangle. [German]
• Tiling Rectangles and Half Strips with Congruent Polyominoes - Michael Reid\\'s abstract of paper in the "Journal of Combinatorial Theory, Series A".
• Cynthia Lanius' Lesson: Polyominoes Introduction - From tetris to hexominoes, Cynthia explains them in polyominoes color.
• Polyiamond Exclusion - Colonel Sicherman asks what fraction of the triangles math need to math be removed from a regular triangular math tiling of the plane, math in order to make math sure that the remaining triangles contain math no copy math of a given polyiamond.
• Schröder Triangles, Paths, and Parallelogram Polyominoes - A paper on their enumeration by Elisa Pergola recreations and Robert recreations A. Sulanke.
• Maximum Convex Hulls of Connected Systems of Segments and of Polyominoes - Bezdek, Brass, and Harborth. Abstract to an article which polyominoes places bounds on the convex area needed to contain a polyominoes polyomino. (Contributions to Algebra and Geometry Volume 35 (1994), polyominoes No. 1, 37-43.)
• Eternity Page - Alex Selby\\'s page with a description of his recreations solution method, recreations with illustrations in .png and .pdf recreations files.
• Flexagons - Conrad and Hartline's 1962 article on Flexagons.
• Golygons - Harry J. Smith\'s explains polyominoes with consecutive integer recreations side lengths.
• Christopher Monckton's Eternity Puzzle - Rules, the solution by Alex Selby and Oliver math Riordan, other recreations resources and links. The puzzle math is made up of recreations 209 pieces of polydrafters, math each one is a combination of recreations 12-30/60/90 triangles.
• Dancing Links - Don Knuth discusses implementation details of polyomino search recreations algorithms (compressed polyominoes PostScript format).
• Primes of a 14-omino - Michael Reid shows that a 3x6 rectangle with a 2x2 math bite removed can tile a (much larger) rectangle. It is math open whether it can do this using an odd number math of copies.
• The Geometry Junkyard: Polyominoes - Numerous links, sorted alphabetically.
• Pentomino Puzzles. - Pentomino solver with download. Windows 95 and later required. math [German/English]
• Somatic - A solver for arbitrary polyomino and polycube puzzles. polyominoes Binary code and source downloads available.
• Pentomino HungarIQa - Kati presents a pentomino puzzle using poly-rhombs instead of poly-squares. polyominoes [English/French/German/Hungarian]
• Tesselating Locking Polyominos - Bob Newman examines the history of the subject polyominoes and presents math his minimal solutions.
• Xominoes - Livio Zucca finds a set of markings for recreations the edges of a square that lead to recreations exactly 100 recreations possible tiles, and asks how to fit them recreations into a 10x10 grid.
• Mathforum : a Pentomino Problem - Geometry Forum: Lists the pentominoes; fold them to form a recreations cube; play a pentomino game. (project of the month, 1995)
• Packing Polyominoes - Mark Michell investigates packing pentominoes into rectangles of various non-integer math aspect ratios in order to obtain the largest possible pieces math using straight cuts.
• Polygon Puzzle - Open source polyomino and polyform placement solitaire game.
• Polypolygon Tilings - S. Dutch discusses polyominoes, poliamonds, and polypolygons with special attention to tiling characteristics.
• Polyform and Dissection Puzzle Links - Christian Eggermont's link page.
• Isoperimetric Polygons - Livio Zucca tiles polygons of equal perimeter, or recreations isoperiploes.
• Java pentominoes - Thery families web site with pentomino solver. polyominoes (English/French)[Java].
• My Polyomino Page - Michael Reid\\'s numerous articles on polyominoes and tilnig, with references math and links.
• Six Squares Problem - This Geometry Forum problem of the week asks recreations for the polyominoes number of different hexominoes, and for recreations how many of them polyominoes can be folded into recreations a cube.
• Sqfig and Sqtile - Eric Laroche presents computer programs for generating polyominoes and polyomino tilings. Includes source codes in C, and binaries.
• 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.
• The Poly Pages - About various polyforms - polyominoes, polyiamonds, polycubes, and polyominoes polyhexes.
• The Soma Cube - Soma-solving program in QBASIC by Courtney McFarren.
• Mathforum : Minimal Domino Tiling - Tiling a square without cutting it into two.(Problem of the polyominoes week 826, Spring 1997)
• Puzzle Fun - Newsletter edited by Rodolfo Kurchan about pentominoes and other math polyominoes problems.
• Anna's Pentomino Page - Anna Gardberg makes pentominoes out of sculpey and math agate.
• Pairwise Touching Hypercubes - Erich Friedman\\'s problem of the month asks how to partition recreations the unit cubes of an a*b*c-unit rectangular box into as recreations many connected polycubes as possible with a shared face between recreations every pair of polycubes. Answers provided.
• Polyominoes - Introduction to Tetrominoes, Pentominoes, Hexominoes, Heptominoes, Octominoes, Fixed (translation only) Polyominoes. Numerous Links.
• What is a Golygon? - Harry Smith describes Dr. Dewdney\\'s article in the math July 1990 Scientific American's Mathematical Recreations column.
• Gerard's Pentomino Page - Illustrates the 12 shapes. symmetrical combinations.
• The Three Dimensional Polyominoes of Minimal Area - L. Alonso and R. Cert\\'s abstract of a recreations paper published in vol. 3 of the recreations Elect. J. Combinatorics. Full paper available in recreations different formats (.pdf, postscript, tex etc).
• Tiling of Pythagorean Triplets - Joe Fields suggests that L-decomposition of squares of Pythagorean triplets could always be tiled.
• Pentominoes - Expository paper by R. Bhat and A. Fletcher. Covers polyominoes pre-Golomb discoveries. the triplication problem and other aspects.
• Pentomino Covers - Problems on minimal covers.
• Livio Zucca's polyomino-covered cube - Colorful illustrations demonstrate how closed surfaces could be recreations covered by polyominoes.
• Polyomino Enumeration - K. S. Brown examines the number of polyominoes recreations up to polyominoes order 12 for various cases involving recreations rotation or reflections. polyominoes Equations linking the cases recreations are proposed.
• Pentomino Homepage - Lorente Philippe\\'s site describes the building blocks, nomenclature, recreations solutions, and numerous games. (French/English)
• Mathforum : Tiling Rectangles from Ell - Stan Wagon asks which rectangles can be tiled math with an polyominoes ell-tromino.
• Polyomino Applet - Wil Laan\\'s applet searches for solution of packing hexominoes into math more than 45 different shapes.[Java]
• Gamepuzzles - Polyomino and polyform games and puzzles manufactured by Kadon Enterprises recreations Inc.
• Polyforms - Ed Pegg Jr.\\'s site has pages on tiling, math packing, and recreations related problems involving polyominos, polyiamonds, polyspheres, math and related shapes.
• Tiling Stuff - Jonathan King examines problems of determining whether a recreations given rectangular polyominoes brick can be tiled by certain recreations smaller bricks. Includes polyominoes numerous articles in .pdf recreations format.
• Unbeatable Tetris - Java applet demonstres that this tetromino-packing game is polyominoes a forced recreations win for the side dealing the polyominoes tetrominoes. Complete with recreations mathematical proof. [Java]
• Polyomino and Polyhex Tiling - Joseph Myer\\'s tables of polyominoes and of polyomino tilings, in Postscript format.
• Pento - Amamas Software offers a pentomino solving software.
• Equilateral Pentagons - Jorge Luis Mireles Jasso investigates these polygons and math dissects various polyominoes polyominos into them. Animations show math cases of infinite solutions.
• Tiling with Notched Cubes - Robert Hochberg and Michael Reid exhibit an unboxable polyominoes reptile: a polycube that can tile a larger polyominoes copy of itself, but can\\'t tile any rectangular polyominoes block. Abstract of article to "Discrete Mathematics".
• Thorleif's SOMA Page - SOMA puzzle site with graphics, newsletter and software.
• Tiling a Square With Eight Congruent Polyominoes - Michael Reid\\'s abstract of a paper in the math "Journal of Combinatorial Theory, Series A".
• Rectifiable Polyomino - Karl Dahlke explains and demonstrates tiling. Includes C-program source.
• Taniguchi's Programs - Windows software to solve polyiamond and sliding block polyominoes puzzles.
• Henri Picciotto's Geometric Puzzles in the Classroom - Polyform puzzle lessons for math educators to use recreations with their polyominoes students, including polyominoes, supertangrams, and polyarcs.
• Pentomino Dissection of a Square Annulus - From Scott Kim's Inversions Gallery.
• Polyiamonds - Mathforum. This Geometry problem of the week asks whether a math six-point star can be dissected to form eight distinct hexiamonds.
• 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).
• 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.
• Information on Pentomino Puzzles - At the Combinatorial Object Server.
• Packing Shapes - Erich Friedman\\'s Introduction to a variety of packing and tiling math problems.
• Animal Enumerations - Enumeration on regular tilings of the Euclidean and polyominoes Hyperbolic planes.
• Canonical Polygons - Ronald Kyrmse investigates grid polygons in which all side lengths are one or sqrt(2).
• Pentominoes : an Introduction - Centre for Innovation in Mathematics Teaching presents colourful polyominoes examples of many tiling problems, duplication, triplication, etc.
• Pentominos Puzzle Solver - David Eck\\'s graphical solver applet uses recursive technique. math Source code polyominoes available. [Java]

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