A project inspired by an AMC 12 octagon problem

The problem pictured below from the 2003 AMC 12 gave my son some trouble:

We talked through it together a few days ago, but I thought it would be fun to try to do an octagon-inspired math project today.

We started with the problem and then talked a bit about a 3d print we found on Thingiverse:

Next we took a look at a version of the 3d printed shape that we made from our Zometool set. You can’t make a regular octagon with a Zometool set, and the fact that our shape didn’t have a regular octagon led to a good discussion:

For the last part of the project we tried to find the volume of our truncated cube.