There are so many star blocks to choose from but I have selected spinning stars because of the unusual construction. Many stars are based on an eight pointed diamond in the centre but this star has an octagon. It is surrounded by triangles which appear to be spinning. This whole section is then inserted as the centre of another star.

Figure 1: Spinning Star
 
To construct the block see Figure 1. Starting with the centre octagon add one triangle making sure to leave part of the seam unsewn. Working anti clockwise keep adding triangles until you get back to the first triangle. You will now be able to complete the partial seam. Now add the smaller triangles to the four corners. The points are constructed by adding the smaller triangle to the four sided shape and then sewing this unit to the large triangle. Note that this is a rectangle not a square when it is finished. The block can then be assembled as shown.

Figure 2: Spinning Star Layout
 
When the blocks are assembled edge to edge a double pattern of small squares on point and larger squares appears where the blocks join, see Figure 2. These can be used to add interest in the quilting perhaps small stars. Alternatively you could decide to use different fabrics in the corners and thus create a checkerboard effect.
 

Figure 3:
Alternative blocks
We have provided templates for a 12in block. For alternative unusual star blocks see Figure 3. Stars and chains and Star of Bethlehem both start with an eight pointed star in the centre but the addition of either squares or triangles creates a different frame, the pink diamonds followed by the dark blue triangles in Stars and chains create a floating effect of two squares overlapping, this could be emphasised by changing four of the triangles to a slightly lighter shade. The Star of Bethlehem block without the four corner triangles is an octagon. This could be used as the centre of a much enlarged spinning star block, creating a quilt top from one block. In the Liberty star block, the eight pointed star itself is created from strips. These could be strip pieced first and then the diamonds cut from the resulting material. All of these blocks need careful attention to seams as many are inset and have bias edges which are much more likely to stretch and distort.