The geometry of 4-dimensional space is much more complex than that of 3-dimensional space, mostly due to the extra degree of freedom.
In 3-dimensional space there are three orthogonal coordinate axes — usually labeled x, y, and z. The six cardinal directions in this space can be called up, down, east, west, north, and south. Positions along these axes can be called altitude, longitude, and latitude. Lengths measured along these axes can be called height, width, and depth.
However, 4-dimensional space has an extra orthogonal coordinate axis, which is usually labeled w. Hinton, our smart Irish lad from the 1880s described the two additional cardinal directions as ana and kata, from the Greek words meaning “up toward” and “down from”, respectively. However, this is a very restricted and particular space to work within.
I am tired now. I haven’t thought about this stuff in 30 years and it is giving me nightmare flashbacks, especially thinking of non-Euclidean spaces.