Tessellation Symmetry, Page 1 of 6: Introduction

In a tessellation, there is repeating. The repeating makes a pattern.

At right we see two of the three ways a shape can repeat: "reflecting" and "rotating", also known as "flipping" and "turning".

In the top picture the whales are in a line facing one way, and then in a line facing the other way. That combination is one pattern. We call that pattern "reflection symmetry", or "flipping".

In the other picture the shapes gather and rotate around a few center-points. That's another kind of pattern. We call that pattern "rotational symmetry", or "turning".

For flat stuff...what your math teacher would call "2D planes" and your department store would call "wallpaper"...there are only a few possible patterns. We know of only 17 kinds of symmetry patterns for flat areas! We call these "the 17 symmetry patterns", or just "the 17 wallpaper groups". I think "the 17 wallpaper groups" sounds much friendlier.

Do you want to see a list of those 17 symmetry patterns" ?...Ummm... I mean, "the 17 wallpaper groups" ? OK, Click here to see the Pólya illustration in the Escher section of our website. When you're done, come back to this page and read more about symmetry.