Editing Polyform (section)

==Types and applications==
Polyforms are a rich source of problems, [[puzzle]]s and [[game]]s. The basic [[combinatorial]] problem is counting the number of different polyforms, given the basic polygon and the construction rules, as a function of ''n'', the number of basic polygons in the polyform.

{| class=wikitable
|+ Regular polygons
|-
!Sides
!colspan="2"|Basic polygon (monoform)
!width=170|Monohedral<BR>tessellation
!Polyform
!Applications
|-
!3
![[image:Monoiamond.png]]
|[[Triangle#Types of triangle|equilateral triangle]]
|[[File:Uniform triangular tiling 111111.png|80px]]<BR>[[Deltille]]
|[[Polyiamond]]s: moniamond, diamond, triamond, tetriamond, pentiamond, hexiamond
|[[Blokus Trigon]]
|-
!4
![[image:Monomino.png]]
|[[Square (geometry)|square]]
|[[File:Square tiling uniform coloring 1.svg|80px]]<BR>[[Square tiling|Quadrille]]
|[[Polyomino]]s: monomino, [[Domino (mathematics)|domino]], [[tromino]], [[tetromino]], [[pentomino]], [[hexomino]], [[heptomino]], [[octomino]], [[nonomino]], [[decomino]]
|[[Tetris]], [[Fillomino]], [[Tentai Show]], [[Ripple Effect (puzzle)]], [[LITS]], [[Nurikabe (puzzle)|Nurikabe]], [[Sudoku]], [[Blokus]]
|-
!6
![[image:Monohex.png]]
|[[Hexagon|regular hexagon]]
|[[File:Uniform tiling 63-t0.svg|80px]]<BR>[[Hextille]]
|[[polyhex (mathematics)|Polyhex]]es: monohex, dihex, trihex, tetrahex, pentahex, hexahex
|
|}

{| class=wikitable
|+ Other polyforms
|-
!Sides
!colspan="2"|Basic polygon (monoform)
!width=170|Monohedral<BR>tessellation
!Polyform
!Applications
|-
!1
![[image:Monostick.png]]
|[[line segment]]
|
|[[polystick]]
|[[Display device#Segment displays|Segment Displays]]
|-
!rowspan=2|3
![[image:Monodrafter.png]]
|[[Special right triangles#30–60–90 triangle|30°-60°-90° triangle]]
|[[File:1-uniform 3 dual.svg|80px]]<BR>[[Kisrhombille tiling|Kisrhombille]]
|[[polydrafter]]
|[[Eternity puzzle]]
|-
![[image:Monoabolo.png]]
|[[Special right triangles#45–45–90 triangle|right isosceles (45°-45°-90°) triangle]]
|[[File:1-uniform 2 dual.svg|80px]]<BR>[[Kisquadrille]]
|[[polyabolo]]
|[[Tangrams]]
|-
!4
![[Image:Monominoid.svg|60px]]
|[[rhombus]]
|[[File:Rhombic star tiling.svg|80px]]<BR>[[Rhombille]]
|[[polyrhomb]]
|
|-
!4
!
|Joined Half-Squares
|
|[[Polyare]]
|
|-
!12
!
|Joined Half-Cubes
|
|[[Polybe]]
|
|-
!5
![[Image:Pentagonal Cairo Snub Square Tile.svg|60px]]
|[[Cairo pentagonal tiling|Cairo Pentagon]]
|
|[[Polycairo]]
|
|-
!12
![[Image:Hexahedron.svg|60px]]
|[[Cube]]
|
|[[Polycube]]
|[[Soma cube]], [[Bedlam cube]], [[Diabolical cube]], [[Slothouber–Graatsma puzzle]], [[Conway puzzle]]
|-
!4
!
|Joined Half-Hexagons
|
|[[Polyhe]]
|
|-
!4
!
|[[Kite_(geometry)|60°-90°-90°-120° Kite]]
|
|[[Polykite]]
|
|-
!4
![[image:Monomino.png]]
|Square (Connected at Edges or Corners)
|
|[[Polyplet]]
|
|-
!3
!
|30°-30°-120° Isosceles Triangle
|
|[[Polypon]]
|
|-
!4
!
|[[Rectangle]]
|
|[[Polyrect]]
|
|}