Similarly, a polyiamond is a figure formed by adjoining equilateral triangles edge to edge. The term is T. H. O'Beirne's etymologically unsound generalization of diamond. A polyhex is a figure formed by adjoining regular hexagons edge to edge. More generally, a polyform is a figure formed by adjoining congruent cells.
Here I present some pages about polyforms.
No room! No room!they cried out when they saw Alice coming.
The exclusion problem is to remove as few cells from the plane as possible so as to exclude a given polyform.
 | Polyiamond Exclusion. A study of the exclusion problem for polyiamonds. |
 | Polyhex Exclusion. A study of the exclusion problem for polyhexes. |
 | Zucca's Challenge Problem. Given two sets of polyforms, construct a figure that can be tiled with any member of the first set and no member of the second. |
 | Pentomino Compatibility. Given two pentominoes, construct a figure that can be tiled with either. |
 | Hexiamond Compatibility. Given two hexiamonds, construct a figure that can be tiled with either. |
 | Heptiamond Compatibility. Given two heptiamonds, construct a figure that can be tiled with either. |
 | Octiamond Compatibility. Given two octiamonds, construct a figure that can be tiled with either. |
| Mixed Polyiamond Compatibility. Given two polyiamonds of different orders, construct a figure that can be tiled with either. |
 | Pentahex Compatibility. Given two pentahexes, construct a figure that can be tiled with either. |
 | Pentahex Odd Pairs. Given two pentahexes, construct a figure that can be tiled with an odd number of either. |
 | Mixed Polyhex Compatibility. Given two polyhexes of different orders, construct a figure that can be tiled with either. |
 | Five Euphoric Pentahexes. Each of these pentahexes is compatible with all 82 hexahexes. |
 | Three Euphoric Hexahexes. Each of these hexahexes is compatible with all 82 hexahexes. |
 | Tetrabolo Compatibility. Given two tetraboloes, construct a figure that can be tiled with either. |
 | Tetracube Compatibility. Given two tetracubes, construct a figure that can be tiled with either. |
 | Tetrominoes Challenge Update. Two better solutions for Livio Zucca's Tetrominoes Challenge. |
 | Triple Pentominoes Update. New and improved solutions for Livio Zucca's Triple Pentominoes. |
 | Pentomino Odd Pairs Update. Improved solutions for Livio Zucca's Pentomino Odd Pairs. |
 | Cell Shifts for Polyominoes of order up through 6. |  | Cell Shifts for Pentomino Pairs. |
 | Cell Shifts for Polyhexes of order up through 5. |  | Cell Shifts for Pentahex Pairs. |
 | Cell Shifts for Heptominoes. |  | Cell Shifts for Hexahexes. |
 | Cell Shifts for Polyiamonds of order up through 7. |  | Cell Shifts for Heptahexes. |
 | Cell Shifts for Octiamonds. |
That is another of your odd notions,said the Prefect, who had the fashion of calling everything
oddthat was beyond his comprehension, and thus lived amid an absolute legion of
oddities.
The Purloined Letter
An oddity is a figure with binary symmetry made by joining an odd number of copies of a polyform.
 | Polyomino Oddities. Oddities for polyominoes of order up to 7. |
 | Pentomino Oddities. Pentomino oddities with specific symmetries. |
 | Hexomino Oddities. Hexomino oddities with specific symmetries. |
 | Polyomino Semi-Oddities. Semi-oddities for polyominoes. A semi-oddity is a figure with quaternary symmetry and an even number of tiles that is not a multiple of 4. |
 | Heptomino Oddities. Heptomino oddities with specific symmetries. |
 | Pentaking Oddities. Oddities with specific symmetries for pseudopolyominoes of order 5. |
 | Pentiamond, Heptiamond, and Enneiamond Oddities. Oddities for pentiamonds, heptiamonds, and enneiamonds. Oddities for polyiamonds of odd order can have only bilateral symmetry. |
 | Hexiamond Oddities. Hexiamond oddities with specific symmetries. |
 | Octiamond Oddities. Octiamond oddities with specific symmetries. |
 | Polyiamond Tri-Oddities. These are like oddities but with ternary symmetry. |
 | Polyhex Oddities. Oddities for polyhexes of order up to 5, with specific symmetries. |
 | Hexahex Oddities. Hexahex oddities with specific symmetries. |
 | Heptahex Oddities. Heptahex oddities with specific symmetries. |
 | Polyhex Tri-Oddities. Tri-oddities for polyhexes of order up to 5. |
 | Hexahex Tri-Oddities. Tri-oddities for hexahexes. |
 | Heptahex Tri-Oddities. Tri-oddities for heptahexes. |
 | Pentapent Oddities. Oddities for pentapents. |
 | Pentahept Oddities. Oddities for pentahepts. |
 | Polyoct Oddities. Oddities for polyocts of order 1 through 5. |
 | Pentenn Oddities. Oddities for pentenns. |
 | Catalogue of Polypents. Enumerations and pictures of these neglected polyforms. |
 | Catalogue of Polyhepts. Some more neglected polyforms. |
 | Catalogue of Polyocts. Still more neglected polyforms. |
 | Polycube Symmetries. In how many ways can a polycube be symmetrical? |
 | Printable Grid Files. Triangular and hexagonal grids, for those who like to play with polyiamonds and polyhexes. |
 | Tetromino Wallpaper. |
 | Pentiamond Wallpaper. |
 | Tetrahex Wallpaper. |
 | Dragomino Wallpaper. A Dragomino is the polyomino equivalent of a Dragon Curve. |
| Polyiamonds, at Mathematische Basteleien (in German) |
| Miroslav Vicher's Polyiamonds Page |
| Andrew Clarke's The Poly Pages |
| Iamonds at Ed Pegg's mathpuzzle.com |
| Polyominoes and Other Animals at The Geometry Junkyard |
| Polyiamond at MathWorld |
| Livio Zucca's Remembrance of Software Past |
| Gabriele Carelli's Polyforms (in Italian) |
| The September 2004 issue of Erich Friedman's Math Magic, on polyform compatibility. |
| The November 2004 issue of Erich Friedman's Math Magic, on Galvagni's Multiple Tiling Problem. |
| Peter's Polyform Pages. |
| Michael Reid's Polyomino Page. |
| Giovanni Resta's Polypolyominoes. |
| Jorge Luis Mireles's Poly2ominoes. |
| KSO Glorieux Ronse's Pentomino site, established by Odette De Meulemeester. |
 | Many of my constructions were found using the computing resources of Netrics. |
