On a two-dimensional Cartesian plane we can naturally subdivide the space into four quadrants at the origin. In three-dimensions, the partition into eight parts are known as octants. In four-dimensional space we have sixteen parts; what is the corresponding name for each partition?
Wikipedia has an n-dimensional name:
In geometry, an orthant or hyperoctant is the analogue in n-dimensional Euclidean space of a quadrant in the plane or an octant in three dimensions.
Even if it isn't common usage, what would the next term be for 4-dimensions (of sixteen parts)?