Polyform Puzzles

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Many puzzles and games have been proposed for different polyforms. Some use complete sets, others use multiple copies of a single piece.

Here are some of the general types of puzzle which have been invented. Some of these puzzles have been studied extensively, with complete sets of solutions published for a given set of pieces. However, the same puzzle with different pieces may not have been investigated at all. Several books and papers have been written about the pentominoes and there is much information available online too, but that does not mean that you cannot come up with something new.

The shapes which are possible will depend upon the geometry of the pieces, so where necessary I will give a couple of examples.

Puzzles using complete sets or copies of the same tile(s)

Puzzle Type Description Examples  
Geometric Forms

Construction of simple geometric shapes.

Rectangles with polyominoes.

Hexagons with polyiamonds.

 

Iconic Constructions which resemble animals, trees, buildings, cars etc. Pentomino Zoo  
Portholes Constructions containing the maximum number of unit holes. Tetrahex Portholes, Pentahex Portholes  
Farms or Fences Constructions containing a single hole of maximal area.    
Houses Constructions containing holes of specific shapes. Often the hole shapes are polyforms of the same set or group.

Penthouses with polyominoes.

 
Paths Constructions of the longest path. Variations include mazes and paths formed from the negative space. Polyomino Mazes  
Replication Constructions of copies of a shape, each using a fraction of the set. Sextuplets .  Hexahex Nonets  
Replication 2

Constructions of a symmetric shape from one or more pieces, with the remainder used to make copies of a different shape. Butterflies, dragonflies, propellers and snowflakes are variations on this theme.

Tetrahex Butterflies A, Pentomino Butterflies  
Topological Tiling Tiling the plane, cylinder, torus, Mobius strip, Klein bottle and projective plane Wallpaper Patterns   
Solid Surface Tiling Tiling the faces of a 3 dimensional solid. Flexominoes and flexahexes are variations.

Tiling the faces of a cube with pentominoes  .

Flexominoes . Flexahexes .

 

Puzzles using multiple copies of the same tile(s)

Puzzle Type Description Examples  
Geometric Forms

Construction of simple geometric shapes. Polyominoes which can make a rectangle are said to be rectifiable.

Rectangles with polyominoes.

Hexagons with polyiamonds.

 

Topological Tiling Tiling the plane, cylinder, torus, Mobius strip, Klein bottle and projective plane  

 

Compatibility

Shapes which can be made from copies of one tile, and duplicated using copies of another, or the same tile in a different arrangement.

Galvagni, Reid & Plover Figures

 
Oddities

Symmetric shapes which can be made from an odd number of copies of one tile.

Oddities

 
     

 

 

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