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.
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. |
 | 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. |
| 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. |
 | 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. |
 | Triple Pentominoes Update. New and improved solutions for Livio Zucca's Triple Pentominoes. |
 | Tetrominoes Challenge Update. Two better solutions for Livio Zucca's Tetrominoes Challenge. |
 | Tetracube Compatibility. Given two tetracubes, construct a figure that can be tiled with either. |
 | Galvagni Figures and Reid Figures for Pentominoes. These figures can be tiled with a pentomino in two or more ways with or without holes. |
 | Galvagni Figures and Reid Figures for Hexominoes. These figures can be tiled with a hexomino in two or more ways with or without holes. |
 | Galvagni Figures and Reid Figures for Heptiamonds. These figures can be tiled with a heptiamond in two or more ways with or without holes. |
 | Galvagni Figures and Reid Figures for Octiamonds. These figures can be tiled with an octiamond in two or more ways with or without holes. |
 | Galvagni Figures & Reid Figures for Pentahexes. These figures can be tiled with a pentahex in two or more ways with or without holes. |
 | Galvagni Figures & Reid Figures for Hexahexes. These figures can be tiled with a hexahex in two or more ways with or without holes. |
 | Galvagni Figures & Reid Figures for Heptahexes. These figures can be tiled with a heptahex in two or more ways with or without holes. |
 | Galvagni Figures & Reid Figures for Octahexes. These figures can be tiled with an octahex in two or more ways with or without holes. |
 | Plover Figures for Polyiamonds and Polyhexes. These figures can be tiled with a polyiamond or a polyhex in two or more ways without flipping it over. |
 | Galvagni Figures for Pentacubes. These figures can be tiled with a pentacube in two or more ways. |
 | Cell Shifts for Polyominoes of order up through 6. |  | Cell Shifts for Polyhexes of order up through 5. |
 | 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. |
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 various symmetries. |
 | Hexomino Oddities. Hexomino oddities with various symmetries. |
 | Pentaking Oddities. Oddities with various 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 various symmetries. |
 | Octiamond Oddities. Octiamond oddities with various symmetries. |
 | Polyiamond Tri-Oddities. These are like oddities but with ternary symmetry. |
 | Polyhex Oddities. Oddities for polyhexes of order up to 5, with various symmetries. |
 | Hexahex Oddities. Hexahex oddities with various symmetries. |
 | Heptahex Oddities. Heptahex oddities with various 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. |
 | Catalogue of Polypents. Enumerations and pictures of these neglected polyforms. |
 | 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 |
| 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. |
