Hi Mark, welcome and congratulations...wow that thing is freaking beautiful!
I think the body shape, with its extended upper horn and slight offset at the neck to improve balance, is in between the traditional omega and the Balance K. This might be called a Balance Point. Mica will likely verify and provide more info when she gets a chance.
For now, here is some information I found that was included with one of the postings online when it was for sale:
Alembic Series II 5 string
34" scale
Bookmatched Cocobolo top
Bookmatched Cocobolo back
7-piece maple, purple heart and ebony long scale neck
Custom neck taper (1.8 x 2.5)
Side LED's in red, inlaid in sterling silver
Alalone oval fretboard inlays
Crown peghead shape
Heart omega carving
Tummy and elbow contours
24 karat gold plated hardware
Inlaid solid bronze logo with mother of pearl and abalone, including abalone rays
Recessed gold straplocks
Series II pickups and electronics
Comes with original G&G case, DS-5R, papers, strap locks, tools, 5-pin cable and 4 sets of Ken Smith Strings.