Determine the symmetry group of the tessellation of the plane exemplified by the brickwork shown

step 1 In answering this question, we need to appreciate that the symmetry elements of every triangle c

Determine the symmetry group of the tessellation of the...

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Key Concepts

Wallpaper Groups

Wallpaper groups provide a classification scheme for two-dimensional repetitive patterns based on their symmetries. There are 17 distinct wallpaper groups which capture all the possible combinations of isometries that can occur in a periodic tiling of the plane, making them central to the study of planar symmetry.

Isometries in the Euclidean Plane

Isometries are distance-preserving transformations in the Euclidean plane. They include translations (sliding), rotations (turning about a point), reflections (flipping across a line), and glide reflections (a translation combined with a reflection). These operations are crucial for understanding how patterns like tessellations can be mapped onto themselves.

Tessellation

A tessellation is a pattern of shapes that covers a plane without gaps or overlaps. It involves repeating a basic shape or group of shapes using isometries, such as translations and rotations, to fill the entire plane in a regular, periodic manner.

Symmetry Group

The symmetry group of a pattern consists of all the isometries under which the pattern remains unchanged. This includes transformations like translations, rotations, reflections, and glide reflections, and it provides a way to classify and analyze the invariance properties of the tessellation.

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