"Spaceship Earth" at Disney's Epcot Center in Orlando, Florida is a good example of isometries you see in the real world. Start with a triangle, then rotate it 120 degrees to form a second triangle, and then rotate once again to form a third triangle. This rotated triangle pattern is then duplicated until it covers the entire "Spaceship Earth."
Photo copyrighted by Mary Rolfe. www.pansophist.com/se.htm