Can you show this. I have an idea that items would fail a vertical line test to occupy all eight octants in 3d simultaneously.
Let r be an arbitrary curve in R^2 ( second dimension). Suppose r is rigidly transformed into a curve r* that lines in R^3. Show that r* cannot lie in all octants of R^3 simultaneously.
Let r be an arbitrary curve in R^2 ( second dimension). Suppose r is rigidly transformed into a curve r* that lines in R^3. Show that r* cannot lie in all octants of R^3 simultaneously.