### Sites 58

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].

Animal Enumerations

Enumeration on regular tilings of the Euclidean and Hyperbolic planes.

Anna's Pentomino Page

Anna Gardberg makes pentominoes out of sculpey and agate.

Blocking Polyominos

Rodolfo Kurchan searches the smallest polyomino such that a particular number of 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).

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.

Dancing Links

Don Knuth discusses implementation details of polyomino search algorithms (compressed PostScript format).

Flexagons

Conrad and Hartline's 1962 article on Flexagons.

Gamepuzzles

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.

Knight's Move Tessellations

Dan Thomasson looks at tesselations with numerous unexpected shapes traced out by knight moves.

Lego Pentominos

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).

Packing Shapes

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.

Pento-Mania

Pentomino based puzzle game lets children solve and create geometric puzzles. Win32 software, try or buy.

Pentomino Applet

Rujith de Silva's applet puzzle offers games of four different sized rectangles. Source code available. [Java]

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 HungarIQa

Kati presents a pentomino puzzle using poly-rhombs instead of poly-squares. [English/French/German/Hungarian]

Pentomino Relationships

Symmetries in the families of rectangular solutions.

Pentominoes

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.

Pentominos

Graphics problems, solutions (including animated GIF) and links. (English/German through main page)

Pentominos

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.

Polyform Curiosities

Topics include exclusion, compatibility, and wallpaper. Includes examples and charts.

Polyforms

Ed Pegg Jr.'s site has pages on tiling, packing, and related problems involving polyominos, polyiamonds, polyspheres, and related shapes.

Polygon Puzzle

Open source polyomino and polyform placement solitaire game.

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.

Polyomino and Polyhex Tiling

Joseph Myer's tables of polyominoes and of polyomino tilings, in Postscript format.

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.

Polyominoes

Describes a numerical invariant that can be used to classify polyominoes.

Polypolygon Tilings

S. Dutch discusses polyominoes, poliamonds, and polypolygons with special attention to tiling characteristics.

Puzzle Fun

Newsletter edited by Rodolfo Kurchan about pentominoes and other math problems.

Rectifiable Polyomino

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.

Somatic

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.

Taniguchi's Programs

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).

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.

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]

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February 13, 2015 at 7:15:08 UTC
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