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 |
|
| |
|
|
|
|