Starting with your form intersections, though your lines are somewhat faint here, you've done an excellent job in demonstrating a strong grasp of how these forms exist together within the same space, as well as how they relate to one another within that space. You've demonstrated some very strong spatial reasoning skills here, and while the curved-on-curved intersections can definitely be drawn a little more confidently (they're a little more timid than the corrections I marked out here), you're showing a clear understanding of how to approach them as well.

Continuing onto your constructions for this lesson, by and large you've done a good job. This lesson focuses primarily on the concept of precision, which is something that we've been fairly lax on up until this point, approaching our constructions by slapping a new form on and dealing with it, rather than planning it out ahead of time.

Precision is often conflated with accuracy, but they're actually two different things (at least insofar as I use the terms here). Where accuracy speaks to how close you were to executing the mark you intended to, precision actually has nothing to do with putting the mark down on the page. It's about the steps you take beforehand to declare those intentions.

So for example, if we look at the ghosting method, when going through the planning phase of a straight line, we can place a start/end point down. This increases the precision of our drawing, by declaring what we intend to do. From there the mark may miss those points, or it may nail them, it may overshoot, or whatever else - but prior to any of that, we have declared our intent, explaining our thought process, and in so doing, ensuring that we ourselves are acting on that clearly defined intent, rather than just putting marks down and then figuring things out as we go.

In our constructions here, we build up precision primarily through the use of the subdivisions. These allow us to meaningfully study the proportions of our intended object in two dimensions with an orthographic study, then apply those same proportions to the object in three dimensions.

While there are a few spots where you could have pushed that precision a little further - for example in the placement of the ports/slots on this construction, and the placements of the clasps on this trunk, I think this is something that you still largely did a great job with, especially with how you leveraged the subdivision throughout constructions like this awesome chest of drawers. I'm especially pleased with how you took advantage of certain cases where you could hinge off the diagonals rather than needing to pin down every orthogonal proportion in order to place your elements (like the drawers and on the wheel of your ipod).

As to your globe, that's honestly how I would have approached it too. A box for the base makes sense, but the bounding box we might use in most other situations is really just one of a few primitives we can use to represent an enclosure of space - and generally the one that is best suited to subdividing and kind of carving it down. But if no such carving is necessary, then how you've approached it here is perfectly fine.

Unfortunately as to your glass, I may not really have a satisfying answer, because it's simply outside of the scope of this course. As you noted yourself, if it were simply a matter of dividing it up into thirds along the base, that'd be fine - but unfortunately thanks to high school trigonometry, we know that the corner portions are right angle triangles, and their hypotenuse which corresponds with the diagonal corner of our octagon would be longer than the outer "thirds" of our subdivided square.

In order to create an octagon, most demonstrations I've seen involve using a compass to create an arc from each corner of the square, passing through the center of the square. Where the arcs touch the sides of the box are where you'd put the vertices for your octagon, as shown here.

Given that it requires us to draw arcs with a compass (so in other words, a circle), this is not something we can easily do. It's not impossible - we have techniques for drawing circles in 3D space (which were introduced in the cylinder challenge, and will further be explored in Lesson 7), but in order to draw them we'd still need to know where exactly they intersect with the square's edges, which is exactly what we'd want to draw the circles (or more accurately, ellipses) form.

Conversely, we could draw it out in 2D, and then analyze the proportions that result - it seems to be about 3/10ths on either side, with the octagon's horizontals/verticals taking up about 4/10ths in between - but I'm not sure how accurate that is mathematically, and so we'd still end up with what is likely an imperfect octagon (although one that is a little closer than the equal thirds).

This really shines light on the fact that Drawabox is not a course on plotted perspective. While this lesson and the last one get quite technical in their use of perspective concepts, it is still always holding to the principle that we do not plot back to vanishing points (since they're often far off the page, they're not a reliable tool we'll always have). While these last two lessons emphasize precision, it is still the precision we can achieve given our restrictions, and always towards the goal of each drawing being an exercise in developing your internal model of 3D space rather than instructions on how to solve every spatial problem. Sometimes you will have to delve into proper perspective, if perfection is really required here - although in my experience (speaking as someone who has spent at least some time working professionally as an illustrator and concept artist), perfection is unnoticeable, and has never been required.

That doesn't mean it's not worth learning, however - but it all depends on what your long term goals are.

Anyway! As a whole your work throughout this lesson as been stellar. So, while I apologize I wasn't able to offer a more satisfactory answer to your question, I will be marking this lesson as complete.