Gotta love all these obscure medical props Okay, let's see... I'd gauge the height of it at 10.25", just a 1/2" taller than the TNG Desktop Viewer (great side-by-side comparison seen in the sixth pic posted above).
I figure the base is 3/4" thick beveled acrylic, with the support arm for the three trays being 1/2" thick acrylic. The trays have a 1/4" thick acrylic base with a 1/16" thick acrylic lip with a height of 1/4" wrapping around the curved front edge of each.
The rear edge of each appears to be open, likely to allow for the trays to slide into the grooves cut into the support arm. Still trying to determine the width and depth of the entire assembly. I expect to have a rough template done up tomorrow.