Uh… in the making of…furniture, oh Patty(?).
Where, really? Seriously. The OP said three-dimensional objects, and I’m pretty sure that since Homo Habilus, we’ve been making three-dimensional objects. 
In architecture – and especially in my coordination with my carpenters and craftspeople, we need to talk about this, sensibly and with clarity, literally every day.
We use the terms height, width, and depth. Everybody who works with real objects and people on a job site in my area of the U.S. uses these terms, (when speaking English). Mucking about with longitudinal this and transverse that gets you nowhere – the architects may understand it but nobody else does.
What computer-graphics people dealing with virtual objects – pixels with no real relationship to an actual, universal ground plane – do, I couldn’t say.
But actual 3-D objects have a relationship to a ground plane, and when you have a ground plane (i.e., the real ground), you automatically orient to it; thus things rising normal to that plane are measured in ‘height’. Things in a plane perpendicular to ground obliquely in front of the viewer are rotated to and measured in ‘width’. Things then approaching or receding from the viewer you reference with the metric ‘depth’.
I’ve never found another set of terms that everybody understands.
Generally, I would guess, because with other terms that float around in the industry (like ‘elevation’, and ‘section’) you have to assume a reference plane, and then assume that everybody else is assuming that reference plane. Which leads to trouble. Because they don’t.
The one constant that everyone understands, from top to bottom, is: Where is the ground?
You can take the house away, or this piece of furniture, or that wall…but you can’t take the ground (totally) away. Try as Cargill might.