Permalink Submitted by Anonymous on April 11, 2013

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.

## 4-space orthogonal planes, actually 6 of them.

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.