The polyiamond in the image exhibits 6-fold rotational symmetry, contributing 6 lines of symmetry. Additionally, it possesses 2 lines of bilateral symmetry, resulting in a total of 8 lines of symmetry.
The image you sent shows a polyiamond with 6-fold rotational symmetry. A polyiamond is a geometric shape made up of squares joined edge-to-edge. The specific polyiamond you sent can be constructed by taking six squares and arranging them in a hexagonal shape.
The polyiamond in the image has 8 lines of symmetry.
Here's how we can find them:
Rotational symmetry: As the name suggests, the polyiamond has 6-fold rotational symmetry. This means that if you rotate the shape by 60 degrees increments a total of five times, you will return to the original shape. Each of these rotational increments can be considered a line of symmetry. Therefore, there are 6 lines of symmetry due to rotational symmetry.
Bilateral symmetry: Additionally, the polyiamond has two lines of bilateral symmetry. These are lines that divide the shape into two congruent halves. In the image, these lines would be vertical lines that pass through the center of the hexagon.
Therefore, in total, the polyiamond has 8 lines of symmetry: 6 from rotational symmetry and 2 from bilateral symmetry.