In 4-space there are only four perpendicular (or orthogonal) spaces, namely (w,x,y), (w,x,z), (w,y,z), and (x,y,z). Dimensionality is determined by the shape coordinates one dimension lower than the x-space that is being addressed. In 2-space and 3-space the shapes lower than x-space minus one don't result in enough perpendiculars to be addressed.

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