In the place of a PIN, many phones allow users to choose a pattern to lock their phones. On a 3x3 grid of dots, the user's finger slides across three or four dots to unlock the phone; for the rest of the problem, we'll assume it's three dots. Assume that all patterns that users actually create will have consecutive dots adjacent (horizontally, vertically, or diagonally). So, for example, the upper left corner can only be followed by the middle top, the center dot, or the left middle dot. How many such three-dot patterns are there? (Hint: Use the symmetry of the grid. Which dots behave the same as others?)