Polyforms

thumb|300px|Like most modern sets, this wooden tangram is stored in the square configuration.

thumb|right|upright=1.7|The 12 pentominoes can form 18 different shapes, with 6 of them (the chiral pentominoes) being mirrored.

thumb|200px|The five free tetrominoes. thumb|A snapshot from a typical game of Tetris. A tetromino is a geometric shape composed of four squares, connected orthogonally (i.e. at the edges and not the corners). Tetrominoes, like dominoes and pentominoes, are a particular type of polyomino. The corresponding polycube, called a tetracube, is a geometric shape composed of four cubes connected orthogonally.

thumb|upright=1.4|The 18 one-sided pentominoes, including 6 mirrored pairs

thumb|300px|The 35 free hexominoes

thumb|upright|All 8 one-sided tetracubes – if chirality is ignored, the bottom 2 in grey are considered the same, giving 7 free tetracubes in total thumb|right|A puzzle involving arranging nine L tricubes into a 3×3×3 cube

thumb|200px|right|All possible free trominos A tromino or triomino is a polyomino of size 3, that is, a polygon in the plane made of three equal-sized squares connected edge-to-edge.

thumb|right|A nonomino or Jigsaw puzzle|Jigsaw [[Sudoku puzzle, as seen in The Sunday Telegraph]] A nonomino (or enneomino or 9-omino) is a polyomino of order 9; that is, a polygon in the plane made of 9 equal-sized squares connected edge to edge. The name of this type of figure is formed with the prefix non(a)-. When rotations and reflections are not considered to be distinct shapes, there are 1,285 different free nonominoes. When reflections are considered distinct, there are 2,500 one-sided nonominoes. When rotations are also considered distinct, there are 9,910 fixed nonominoes.

polyomino of order 2; polygon in the plane made of two equal-sized squares connected edge-to-edge

thumb|400px|The 369 free octominoes

thumb|300px|The 108 free heptominoes A heptomino (or 7-omino or septomino) is a polyomino of order 7; that is, a polygon in the plane made of 7 equal-sized squares connected edge to edge. The name of this type is formed with the prefix hept(a)-. When rotations and reflections are not considered to be distinct shapes, there are 108 different free heptominoes. When reflections are considered distinct, there are 196 one-sided heptominoes. When rotations are also considered distinct, there are 760 fixed heptominoes.

thumb|The 18 one-sided pentominoes: polyforms consisting of five squares.

A polyiamond (also polyamond or simply iamond, or sometimes triangular polyomino) is a polyform whose base form is an equilateral triangle. The word polyiamond is a back-formation from diamond, because this word is often used to describe the shape of a pair of equilateral triangles placed base to base, and the initial 'di-' looks like a Greek prefix meaning 'two-' (though diamond actually derives from Greek ἀδάμας – also the basis for the word "adamant"). The name was suggested by recreational mathematics writer Thomas H. O'Beirne in New Scientist 1961 number 1, page 164.

A decomino, or 10-omino, is a polyomino of order 10; that is, a polygon in the plane made of 10 equal-sized squares connected edge to edge. When rotations and reflections are not considered to be distinct shapes, there are 4,655 different free decominoes (the free decominoes comprise 195 with holes and 4,460 without holes). When reflections are considered distinct, there are 9,189 one-sided decominoes. When rotations are also considered distinct, there are 36,446 fixed decominoes.

thumb|A tessellation of all 7 free tetrahexes In recreational mathematics, a polyhex is a polyform with a regular hexagon (or 'hex' for short) as the base form, constructed by joining together 1 or more hexagons. Specific forms are named by their number of hexagons: monohex, dihex, trihex, tetrahex, etc. They were named by David Klarner who investigated them.

200px|right In recreational mathematics, a polyabolo (also known as a polytan or polytrong) is a shape formed by gluing isosceles right triangles edge-to-edge, making a polyform with the isosceles right triangle as the base form. Polyaboloes were introduced by Martin Gardner in his June 1967 "Mathematical Games column" in Scientific American.