Movement A zero-dimensional object cannot move. A one-dimensional object can move in one dimension (the x-axis). A two-dimensional object can move in two dimensions (the x-axis and y-axis). A three dimensional object can move in three dimensions (the x-, y-, and z-axis).
In other words: There are n different ways for an n-dimensional object to move.
Rotation A zero- and a one-dimensional object cannot rotate. A two-dimensional object can rotate in one way (in the xy-plane). A three dimensional object can rotate in three ways (in the xy-, xz-, and yz-plane). And a four dimensional object can rotate in 6 ways (xy-, xz-, yz-, xw-, yw-, and zw-plane).
In other words: There are n(n-1)/2 different ways for an n-dimensional object to rotate.
Now for the question, what do you call the next thing?
I do know that the next thing has some properties if you follow the same pattern. But I have no idea what it is and I was hoping you guys could help me out.
Here are some of the properties that I have extrapolated:
The next thing
A zero-, one- and two-dimensional object cannot do it. A three dimensional object can do it in one way (along xyz). A four dimensional object can do it in four ways (along xyz, xyw, xzw and yzw. And if you want to extrapolate further... an n-dimensional object can do it in n(n-1)(n-2)/6 different ways.
So yeah, what do you call this thing?