B3D-Chapter 5

Irene Klein

Here are some of the things that struck me as interesting…

First, I had never seen the concept of duality in relationship to polyhedra before. It is a great way to relate shapes to each other instead of treating each shape separately. Also, I noticed that duality seemed to have less meaning in 2-D because all shapes are self-dual. Is that true? If so, there really is not a concept of duality in 1-D.

Also, why are there only three regular polytopes in 5-D and higher? I understand how one gets five in 3-D and six in 4-D, but I do not understand the relationship between these dimensions and higher dimensions and the number of polytopes in these dimensions.

Finally, a good exercise would be to construct a fold-out of a cube in a plane and not allow the model to move into three space. But rather, watch how it moves in 2-space, similar to how the folding hypercube moves in three space.