Regarding the pincushion, the shape is called a rhombic hexecontrahedron, a solid with 60 faces...twelve 5 pointed stars as a solid. The true shape uses 63º diamonds, but that makes a much flatter face on the stars. For a pinchshion you might want to use 60º diamonds. There are examples of each on this site.
http://www.personal.psu.edu/axd2/quilt/qlt28.html The easiest way to construct it is to sew the stars into half bowls of 6 stars each, then sew the halves together.