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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 problem. [Java required].
- Enumeration on regular tilings of the Euclidean and Hyperbolic planes.
Anna's Pentomino Page
- Anna Gardberg makes pentominoes out of sculpey and agate.
- Rodolfo Kurchan searches the smallest polyomino such that a particular number of copies can form a blocked pattern. With solutions.
- Ronald Kyrmse investigates grid polygons in which all side lengths are one or sqrt(2).
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.
Counting Horizontally Convex Polyominoes
- Journal of Integer Sequences, Vol. 2 (1999), Article 99.1.8. Defines and counts horizontal convexity.
Cynthia Lanius' Lesson: Polyominoes Introduction
- From tetris to hexominoes, Cynthia explains them in color.
- Don Knuth discusses implementation details of polyomino search algorithms (compressed PostScript format).
- Alex Selby's page with a description of his solution method, with illustrations in .png and .pdf files.
- Conrad and Hartline's 1962 article on Flexagons.
- Polyomino and polyform games and puzzles manufactured by Kadon Enterprises Inc.
The Geometry Junkyard: Polyominoes
- Numerous links, sorted alphabetically.
Gerard's Pentomino Page
- Illustrates the 12 shapes. symmetrical combinations.
Golygons by Mathworld
- What they are, and how to find them.
Harold McIntosh's Flexagon Papers
- Including copies of the original 1962 Conrad-Hartline papers. Abstract, html-pages, or .pdf documents.
Henri Picciotto's Geometric Puzzles in the Classroom
- Polyform puzzle lessons for math educators to use with their students, including polyominoes, supertangrams, and polyarcs.
Hyperbolic Planar Tessellations
- Don Hatch's page on hyperbolic tesselations with numerous illustrations.
Information on Pentomino Puzzles
- At the Combinatorial Object Server.
Knight's Move Tessellations
- Dan Thomasson looks at tesselations with numerous unexpected shapes traced out by knight moves.
- Eric Harshbarger. This puzzle maker says that the hard part was finding legos in enough different colors.
Logical Art and the Art of Logic
- Pentomino pictures, software and other resources by Guenter Albrecht-Buehler.
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.
Mathforum : a Pentomino Problem
- Geometry Forum: Lists the pentominoes; fold them to form a cube; play a pentomino game. (project of the month, 1995)
Mathforum : Minimal Domino Tiling
- Tiling a square without cutting it into two.(Problem of the week 826, Spring 1997)
Mathforum : Tiling Rectangles from Ell
- Stan Wagon asks which rectangles can be tiled with an ell-tromino.
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.)
Miroslav Vicher's Puzzles Pages
- Polyforms (polyominoes, and polyiamonds) graphics, tables and resources (English/Czech).
My Polyomino Page
- Michael Reid's numerous articles on polyominoes and tilnig, with references and links.
- Erich Friedman's Introduction to a variety of packing and tiling problems.
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.
- Pentomino based puzzle game lets children solve and create geometric puzzles. Win32 software, try or buy.
- Fill up a given area using pentomino shapes, rotating and flipping them. Three levels of difficulty.[Java].
- Rujith de Silva's applet puzzle offers games of four different sized rectangles. Source code available. [Java]
- Problems on minimal covers.
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).
Pentomino Dissection of a Square Annulus
- From Scott Kim's Inversions Gallery.
- Kati presents a pentomino puzzle using poly-rhombs instead of poly-squares. [English/French/German/Hungarian]
- Pentomino solver with download. Windows 95 and later required. [German/English]
- Symmetries in the families of rectangular solutions.
- Expository paper by R. Bhat and A. Fletcher. Covers pre-Golomb discoveries. the triplication problem and other aspects.
Pentominoes : an Introduction
- Centre for Innovation in Mathematics Teaching presents colourful examples of many tiling problems, duplication, triplication, etc.
- Graphics problems, solutions (including animated GIF) and links. (English/German through main page)
- B. Berchtold's applet helps tile a 6x10 rectangle. [German]
Pentominos Puzzle Solver
- David Eck's graphical solver applet uses recursive technique. Source code available. [Java]
The Poly Pages
- About various polyforms - polyominoes, polyiamonds, polycubes, and polyhexes.
Polyform and Dissection Puzzle Links
- Christian Eggermont's link page.
- Topics include exclusion, compatibility, and wallpaper. Includes examples and charts.
- Ed Pegg Jr.'s site has pages on tiling, packing, and related problems involving polyominos, polyiamonds, polyspheres, and related shapes.
- Open source polyomino and polyform placement solitaire game.
- 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.
Polyomino and Polyhex Tiling
- Joseph Myer's tables of polyominoes and of polyomino tilings, in Postscript format.
- 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.
- Describes a numerical invariant that can be used to classify polyominoes.
- S. Dutch discusses polyominoes, poliamonds, and polypolygons with special attention to tiling characteristics.
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.
- Newsletter edited by Rodolfo Kurchan about pentominoes and other math problems.
- Karl Dahlke explains and demonstrates tiling. Includes C-program source.
Schröder Triangles, Paths, and Parallelogram Polyominoes
- A paper on their enumeration by Elisa Pergola and Robert A. Sulanke.
- A solver for arbitrary polyomino and polycube puzzles. Binary code and source downloads available.
Sqfig and Sqtile
- Eric Laroche presents computer programs for generating polyominoes and polyomino tilings. Includes source codes in C, and binaries.
- Windows software to solve polyiamond and sliding block puzzles.
Thorleif's SOMA Page
- SOMA puzzle site with graphics, newsletter and software.
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.
Tiling a Square With Eight Congruent Polyominoes
- Michael Reid's abstract of a paper in the "Journal of Combinatorial Theory, Series A".
Tiling Rectangles and Half Strips with Congruent Polyominoes
- Michael Reid's abstract of paper in the "Journal of Combinatorial Theory, Series A".
- Jonathan King examines problems of determining whether a given rectangular brick can be tiled by certain smaller bricks. Includes numerous articles in .pdf format.
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".
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.
- Java applet demonstres that this tetromino-packing game is a forced win for the side dealing the tetrominoes. Complete with mathematical proof. [Java]
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