Ok, now I think we did it.
After a great workshop I had today, Varda joined me to try again the "Four of Spades Bead" which appears in Fig. 14 in Gwen Fisher and Blake Mellor's paper:
"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)
See also the Bead infinitum gallery and kits http://www.beadinfinitum.com/
I think we deciphered it. I am not sure because the connections might be different. We made it into two parts, as I concluded from last time and Varda really helped me with the connection step.
Another happy beading day is almost over!