A hexomino is a polyomino

Polyomino

A polyomino is a plane geometric figure formed by joining one or more equal squares edge to edge. It is a polyform whose cells are squares. It may be regarded as a finite subset of the regular square tiling with a connected interior....

 of order 6, that is, a polygon

Polygon

In geometry a polygon is a flat shape consisting of straight lines that are joined to form a closed chain orcircuit.A polygon is traditionally a plane figure that is bounded by a closed path, composed of a finite sequence of straight line segments...

 in the plane

Plane (mathematics)

In mathematics, a plane is a flat, two-dimensional surface. A plane is the two dimensional analogue of a point , a line and a space...

 made of 6 equal-sized square

Square (geometry)

In geometry, a square is a regular quadrilateral. This means that it has four equal sides and four equal angles...

s connected edge-to-edge. The name of this type of figure is formed with the prefix hex(a)-. When rotation

Rotation

A rotation is a circular movement of an object around a center of rotation. A three-dimensional object rotates always around an imaginary line called a rotation axis. If the axis is within the body, and passes through its center of mass the body is said to rotate upon itself, or spin. A rotation...

s and reflection

Reflection (mathematics)

In mathematics, a reflection is a mapping from a Euclidean space to itself that is an isometry with a hyperplane as set of fixed points; this set is called the axis or plane of reflection. The image of a figure by a reflection is its mirror image in the axis or plane of reflection...

s are not considered to be distinct shapes, there are 35

35 (number)

35 is the natural number following 34 and preceding 36.- In mathematics :35 is the sum of the first five triangular numbers, making it a tetrahedral number....

 different free hexominoes. When reflections are considered distinct, there are 60

60 (number)

60 is the natural number following 59 and preceding 61. Being three times twenty, 60 is called "three score" in some older literature.-In mathematics:...

 one-sided hexominoes. When rotations are also considered distinct, there are 216

216 (number)

216 is the natural number following 215 and preceding 217.Since 216 = 3^3 + 4^3 + 5^3 = 6^3, it is the smallest cube that's also the sum of three cubes . It is also the sum of a twin prime...

 fixed hexominoes.
The figure shows all possible free hexominoes, coloured according to their symmetry group

Symmetry group

The symmetry group of an object is the group of all isometries under which it is invariant with composition as the operation...

s:

• 20 hexominoes (coloured grey) have no symmetry
  Symmetry
  Symmetry generally conveys two primary meanings. The first is an imprecise sense of harmonious or aesthetically pleasing proportionality and balance; such that it reflects beauty or perfection...
  
  .