taking 4-space in a piece wise fashion, it seems there are actually 6 (thats right; 6!!!) planes that are some how maybe mutually orthogonal to one another. Namely if we take four number lines and mark them w, x, y, z then we can construct the sub-space planes; (w,x), (w,y), (w,z), (x,y), (x,z), and (y,z). How can you have 6 mutually perpendicular planes in 4-space? Is it wrong to say that all the planes are mutually perpendicular? 4-space is turning out to be a really cool and interesting place indeed.

taking 4-space in a piece wise fashion, it seems there are actually 6 (thats right; 6!!!) planes that are some how maybe mutually orthogonal to one another. Namely if we take four number lines and mark them w, x, y, z then we can construct the sub-space planes; (w,x), (w,y), (w,z), (x,y), (x,z), and (y,z). How can you have 6 mutually perpendicular planes in 4-space? Is it wrong to say that all the planes are mutually perpendicular? 4-space is turning out to be a really cool and interesting place indeed.