The supernova is a regular figure with 12 points and 24 equal sides.

The supernova is made up of 12 triangles, 6 six-sided figures that look like arrowheads, and 6 ten-sided figures that look something like a head and shoulders.

Since there are 24 pieces in all, each of the small stars must be made up of 8 pieces. Probably, therefore, there will be 4 triangles, 2 arrowheads, and 2 "head and shoulders" shapes in each small star.