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Polyominoes | |||||||
  Christian Eggermont's link page. |
Describes a numerical invariant that can be used to classify polyominoes. |
What they are, and how to find them. |
Windows software to solve polyiamond and sliding block puzzles. |
Thery families web site with pentomino solver. (English/French)[Java]. |
English words that can be written using the pentomino name letters FILNPTUVWXYZ and other related curiosities, including a homage to Georges Perec. (English/French). |
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. |
Topics include exclusion, compatibility, and wallpaper. Includes examples and charts. |
Ronald Kyrmse investigates grid polygons in which all side lengths are one or sqrt(2). |
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. |
From tetris to hexominoes, Cynthia explains them in color. |
Fill up a given area using pentomino shapes, rotating and flipping them. Three levels of difficulty.[Java]. |
Problems on minimal covers. |
Alexandre Owen Muñiz presents the Icehouse set which lends itself to different polyomino coloring games. |
Eric Laroche presents computer programs for generating polyominoes and polyomino tilings. Includes source codes in C, and binaries. |
From Scott Kim's Inversions Gallery. |
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. |
Ed Pegg Jr.'s site has pages on tiling, packing, and related problems involving polyominos, polyiamonds, polyspheres, and related shapes. |
Alex Selby's page with a description of his solution method, with illustrations in .png and .pdf files. |
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. |
Expository paper by R. Bhat and A. Fletcher. Covers pre-Golomb discoveries. the triplication problem and other aspects. |
A solver for arbitrary polyomino and polycube puzzles. Binary code and source downloads available. |
Centre for Innovation in Mathematics Teaching presents colourful examples of many tiling problems, duplication, triplication, etc. |
Erich Friedman's Introduction to a variety of packing and tiling problems. |
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. |
Don Knuth discusses implementation details of polyomino search algorithms (compressed PostScript format). |
Lorente Philippe's site describes the building blocks, nomenclature, solutions, and numerous games. (French/English) |
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.) |
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. |
Numerous links, sorted alphabetically. |
Kevin Gong offers download of his polyominoes games shareware for Windows and Mac. 100 boards are included. A Java version is under development. |
Polyomino and polyform games and puzzles manufactured by Kadon Enterprises Inc. |
Open source polyomino and polyform placement solitaire game. |
Pentomino pictures, software and other resources by Guenter Albrecht-Buehler. |
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). |
Polyform puzzle lessons for math educators to use with their students, including polyominoes, supertangrams, and polyarcs. |
Joseph Myer's tables of polyominoes and of polyomino tilings, in Postscript format. |
Joe Fields suggests that L-decomposition of squares of Pythagorean triplets could always be tiled. |
Rodolfo Kurchan searches the smallest polyomino such that a particular number of copies can form a blocked pattern. With solutions. |
Newsletter edited by Rodolfo Kurchan about pentominoes and other math problems. |
At the Combinatorial Object Server. |
Geometry Forum: Lists the pentominoes; fold them to form a cube; play a pentomino game. (project of the month, 1995) |
Tiling a square without cutting it into two.(Problem of the week 826, Spring 1997) |
Stan Wagon asks which rectangles can be tiled with an ell-tromino. |
David Eck's graphical solver applet uses recursive technique. Source code available. [Java] |
Jonathan King examines problems of determining whether a given rectangular brick can be tiled by certain smaller bricks. Includes numerous articles in .pdf format. |
Michael Reid's abstract of a paper in the "Journal of Combinatorial Theory, Series A". |
Michael Reid's abstract of paper in the "Journal of Combinatorial Theory, Series A". |
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. |
Rujith de Silva's applet puzzle offers games of four different sized rectangles. Source code available. [Java] |
Michael Reid's numerous articles on polyominoes and tilnig, with references and links. |
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". |
Eric Harshbarger. This puzzle maker says that the hard part was finding legos in enough different colors. |
Dan Thomasson looks at tesselations with numerous unexpected shapes traced out by knight moves. |
A paper on their enumeration by Elisa Pergola and Robert A. Sulanke. |
Java applet demonstres that this tetromino-packing game is a forced win for the side dealing the tetrominoes. Complete with mathematical proof. [Java] |
Anna Gardberg makes pentominoes out of sculpey and agate. |
Mr. Confetti presents a Windows and Java game for tangrams, polyominoes, and polyhexes. |
Karl Dahlke explains and demonstrates tiling. Includes C-program source. |
Journal of Integer Sequences, Vol. 2 (1999), Article 99.1.8. Defines and counts horizontal convexity. |
Pentomino based puzzle game lets children solve and create geometric puzzles. Win32 software, try or buy. |
Polyforms (polyominoes, and polyiamonds) graphics, tables and resources (English/Czech). |
Conrad and Hartline's 1962 article on Flexagons. |
Kati presents a pentomino puzzle using poly-rhombs instead of poly-squares. [English/French/German/Hungarian] |
Enumeration on regular tilings of the Euclidean and Hyperbolic planes. |
B. Berchtold's applet helps tile a 6x10 rectangle. [German] |
Including copies of the original 1962 Conrad-Hartline papers. Abstract, html-pages, or .pdf documents. |
Symmetries in the families of rectangular solutions. |
Don Hatch's page on hyperbolic tesselations with numerous illustrations. |
Graphics problems, solutions (including animated GIF) and links. (English/German through main page) |
Illustrates the 12 shapes. symmetrical combinations. |
S. Dutch discusses polyominoes, poliamonds, and polypolygons with special attention to tiling characteristics. |
SOMA puzzle site with graphics, newsletter and software. |
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. |
About various polyforms - polyominoes, polyiamonds, polycubes, and polyhexes. |
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]. |
Pentomino solver with download. Windows 95 and later required. [German/English] |
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