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[Gyperboloid]

OK, "this is it, this is it !"...
Wanted to start this, like, for ages . Being a classic "for ever newbie" I always planned to start a proper modeling-everything-thing learning course ( kind of ), but obviously never did. So, I'm just throwing it on, just like that, at last.
What I'm talking about, is this thread, in which everybody will ( if interested, obviously ) post their way of modeling a specific object. Later , I hope, other disciplines will be added ( rendering, lights, materials, rigging, animatinganim8ing ).
Well, some may say that there is bazillion of dedicated sites, forums, information out there already available like...for ever, but this thread will be specifically Anim8or oriented ( dah, weird, isn't it  ). While, any links, articles  to any generic modeling relative information are welcome, here will be discussed and more importantly, shown, explained how something can be achieved inside Anim8or, by using its tools. Though, don't be confused: this will not be a kind of a copy of the manual. What to click, where to search for is explained in the manual ( well, most of the basics at least ). Here will be discussed the "proper, more efficient way" of using those tools.
Starting with a very basic, yet important part: "sharp edges".In real world nothing is "really sharp".  How do YOU deal with them, speaking from an artistic modeling approach ( for anything CAD related you usually don't bother )?
The way I do it ( probably the wrong way), is with the use of bevel tool, as is, with poly count being increased at minimum on desired edges or with subdivision involved, but again beveling created edge loops.

[mrbeaver.07]

Thanks for advice

[ENSONIQ5]

Nice methodology and I agree it subdivides much better than using the bevel tool directly on the cube's edges.  It's also possible to achieve step 9 a different way, selecting opposing faces and extruding slightly with the 'Extrude Faces Connected' tool.  Once the first opposing pair have been extruded use 'Drag select' to select the next pair so the new narrow faces are also selected.  The resulting topology is the same as step 9 but with fewer steps, a downside being that extrusion changes the overall size of the cube where your method does not.

[Gyperboloid]

Yeap, ENSONIQ5, that "direct" beveling doesn't work with the subdivision because of the triangles ( in some cases pentagons ), that " don't  like" to be subdivided.
As for the Extrude tool, yes, it does the job, as you mentioned, when changing the size of the object is not a problem. Althtough, with the use of shortcuts ( all available ), edge loop ring selection in conjunction with edge connection is pretty fast routine. Any other tool, which deals with edge loops is a way to go ( Extrude, Inset, etc. ). Extremly helpfull whould be if Steve could come up with a tool that would duplicate a selected edge loop and allow the user to slide the entire loop. Something like the Bevel tool, but without changing the geometry. Simply, an " add edge loop " tool.  By the way Steve, SnapToGrid doesn't work well with the Bevel and Inset tools ( maybe with some others too ) 
After a lot of messing around, it seams that one can't go without the use of subdivision. Especially, about objects that have corners in the manner of those of a cube, overlaping quad loops is the only way to get a clean result.
For example, for a cylinder (and objects that have similar geometry ), which has no corners, its more easy to get that rounded edge, with the use of Bevel tool again. It is not even nesessary to subdivide, since more polygons can be used in the first place ( parameters settings ) . But, of course, a few levels of subdivision add significantly to the overall smoothness of the object.