octagons - median
A very classic pattern can be created by combining regular octagons and squares. One can create star patterns by connecting the midpoints of the edges of the octagons. The choice which points are connected defines the resulting pattern. Authors created notation systems for this. The applet below shows so-called 8/2 stars. In them one starts counting from a midpoint of an edge to connect it with the midpoint of the 3rd edge. One con also define the pattern by the angle these line make with the edge.
This pattern is called acute. The two lines in the midpoints of each edge make an angle of 90°. In the acute system the angle is 45°, in the obtuse 135°.