It can be fun to have students find examples of frieze groups or wallpaper groups in their homes and towns. (Check here for additional information, or try your own google search.) These are one-dimensional versions of tessellations that is, the repeating pattern takes place back and forth along a single line. You often see frieze patterns along the borders of walls and ceilings. If you are exploring these ideas in your classroom, you and your students may find it easier to begin with frieze groups. For example, it will tell you why the wallpaper group for my carpet square is named p4mm. (Hint for teachers: When creating the Slide Tessellation it is important that you. This gives them a clear idea on how their cuts will affect their overall shape. The videos cover the two easiest to create. There are 3 types of tessellations rotation, reflection, and translation (or slide). The article also has technical information (near the top) for those who are interested. Here are two videos that will teach you the process. The examples include drawings and photographs of pavings and mosaics, designs on textiles and pottery, and computer generated images. They span cultures across the globe and hundreds of years of time. Rotations always have a center, and an angle of rotation. This Wikipedia page has many beautiful examples of each wallpaper group near the bottom of the page. A good example of a rotation is one 'wing' of a pinwheel which turns around the center point. Can you find different tessellating designs that have the same pattern of symmetries? The wallpaper group of the symmetry patterns on my carpet is named p4mm ( p4m for short) or *442. 1 2 3 4 5 6 7 Take a look at the red shapes in this tessellation. Mathematicians have discovered that there are exactly 17 of these patterns. Symmetries of tessellations fit together in intricate yet predictable patterns.
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