In article <email@example.com>, firstname.lastname@example.org (Daniel A. Asimov) writes:
Re: Tesseract Projected along a main diagonal. Take the points of the tesseracts vertices to be 16 ordered quadruples whose elements were either one or zero (0,0,0,0), (1,0,0,0), (0,1,0,0), etc. Describe these quadruples in terms of 4 unit vectors, the first pointing in the direction of the diagonal and the other 3 perpendicular to the first and each other. Take the vertices described with this basis and eliminate the components pointing in the direction of the diagonal. I believe you are left with ordered triples in a space perpendicular to the diagonal. Sketching it these triples seem to form a rhombic dodecahedron.