Polyominoes

Preface

Well, I suspect which readers will continue reading such description without a figure. So... I've made some interactive polyomino figure for illustration. They're written in Java (beta api). The coffee icon means that the page/link have one or more applets showing polyominoes. A compensatation is that you'll need Netscape 2.x to read these pages. (more info)

These pages are under rewrite. The original page contains similar info, but use my previous version of an applet to show polyomino.

Contents

• Introduction : What is polyomino? (java version)
  • Domino
  • Tromino
  • Tiling square
• Pentominoes
  • Tiling rectangle
  • Tiling 8x8 square with pentominoes:
    • leaving a 2x2 empty square
    • some other cases
  • Triplication problem
  • Pentomino Farms
  • 13 holes problem
• Bigger polyominoes : Hexominoes ...
  • Why hexominoes cannot cover a rectangle?
  • two hexomino patterns

• Beyond 2D : Soma cube (a picture only)
• Polyiamond and Polyhex : polyhex applet (for my own testing only)
• polyomino playground loader

Related links and References

• Collection of Polyomino Problems(and Solutions)
• Pentominos Puzzle Solver
• COS - combinatorial object server. Readers may generate various combinatorial objects online and also get some info. In particular, there is a pentomino puzzle solver for user-defined shape and a polyomino enumerater. and general info on pentomino puzzles
• The Mathematics of Polyominoes by Kevin Gong, who writes the shareware game Polyominoes
• Polyominoes page in Geometry Junkyard of David Eppstein - contains a lot of links, some are more academic-oriented.

• Gerard's Pentomino Page
• Pento - a program to solve the pentominoes problem
• There are also several pages about polyomino / polyiamond in Eric's Treasure Trove of Mathematics
• Polyomino list
• Results by Torsten Sillke - some other puzzles about pentominoes
• Pentominoes - a passage about pentominoes
• Animated gif solution of 3x20 problem of pentomino in Michelle Raymond's homepage at the Geometry Center. Also feature a page on Cellular Automata and the Pentominoes
• Anna's Pentomino Page
• Stefan Wolfrum's Mind Puzzles Page
• Pentomino-Dictionary - there are actually many English words spelt with the pentomino alphabet!

• Logical Art and the Art of Logic
• Object Orientation Game - where you can download an MS Windows application for playing and solving various polyform puzzles, e.g. pentomino and polyomino.
• Many games about polyomino/pentominoes - a list of software by S.T. Han

By the way, this page has been accessed for times.

Aside

You may also visit my pages on magic square. There you may find a beautiful combination of figure and numbers.

Last update : Jul 20 15:30

Comments? Suggestions? Complaints? Drop me an email here ...
arion@susis.ust.hk. philipl@cs.ust.hk.

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