Thanks to Ronit Florence who encouraged me to read G. L. FISHER & B. MELLOR 's article
"Three-dimensional finite point groups and the symmetry of beaded beads" ( Journal of Mathematics and the Arts, Volume 1, Issue 2 June 2007 , pages 85 - 96), I succeeded to make two of the beads appearing in that paper this morning (the Cuboctahedron and the four of spades beads).
You will find the Cuboctahedron in Fig.22 in the paper above and also many other beautiful 3D beaded beads. Additionally, Gwen Fisher and Florence Turnour have a magnificent site with plenty of extraordinary beaded beads - when you can have a look into their site at:
After my third trial trying to decipher this bead, I understood it is very similar to Laura Shea's Plato bead ("The Art of Beadwork" by Valerie Hector p.34-35).
It took me in total a bit more than an hr to make it.