This is an example of cyclical symmetry with a cyclical frequency of 8 (45 degrees per wedge).  The mesh on the left is before morphing and the mesh on the right is after morphing.  The icon for cyclical symmetry is a number of spheres lying perpendicular the symmetry system's selected axis and connected to the origin with lines.  The number of spheres is equal to the number of symmetric wedges. Each cyclical wedge is identical to the others when rotated through an angle (in this case 45 degrees) about the selected axis. The highlighted handle is moved.  Note how only one handle has been selected and how the other seven symmetric handles are automatically moved symmetrically.  This type of symmetry is very useful for objects that repeat at regular intervals about a central point.