Hexomino

A hexomino (or 6-omino) is a polyomino of order 6, that is, a polygon in the plane made of 6 equal-sized squares connected edge-to-edge. The name of this type of figure is formed with the prefix hex(a)-. When rotations and reflections are not considered to be distinct shapes, there are 35 different Free hexominoes. When reflections are considered distinct, there are 60 one-sided hexominoes. When rotations are also considered distinct, there are 216 fixed hexominoes.

Symmetry

The figure shows all possible free hexominoes, coloured according to their symmetry groups:

20 hexominoes (coloured grey) have no symmetry. Their symmetry group consists only of the identity mapping.

6 hexominoes (coloured red) have an axis of mirror symmetry parallel to the gridlines. Their symmetry group has two elements, the identity and a reflection in a line parallel to the sides of the squares.

2 hexominoes (coloured green) have an axis of mirror symmetry at 45° to the gridlines. Their symmetry group has two elements, the identity and a diagonal reflection.

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Hexomino

Symmetry

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