The fourth chapter of B3D introduces objects called simplexes, which flow from a point, to a line, to a triangle, to a triangular pyramid, to 4-D and so on. The book has now discussed hypercubes, 4-spheres/4-balls, and simplexes. What are some other figures that the book has yet to discuss? Can you predict the shapes of these figures in four space?
Page 78 and 79 deal with dimensional data sets. When I was reading this section, I remembered a similar discussion of dimension and data that I read about in Biology(from Biology: Discovering Life by Levine and Miller pp. 101-103). When talking about ecological communities, the aspects of niches were referred to be "multidimensional." In fact, some of the fundamental aspects of niches were graphed on a three dimensional graph.
Another item I found interesting was the relationship and difference
between slicing and projection. However, I had a little bit of
trouble visually picturing a projection of an object. An exercise
to help this would be to draw slices and projections of an object
and compare them. For instance, I believe a cube sliced would
look similar to the pictures on page 43 and 45 of B3D, while
the projection of a cube would look like a square or hexagon,
depending on the orientation by which it is projected.