[Gem]

What that means is, given 4 points on a flat surface, any of those points alone can be anywhere, but because of the dimensional (2D) constraint the equidistant arrangement is impossible, which means in combination of the four there is place which can't be occupied.



Then we could make that a 3D space and accommodate the fourth point, which means all those points could be 'anywhere' again (except where another point is), but if we add a fith point the 'impossible arrangement" reappears so we again have the 'unnoccupiable place".


Then we see that no matter how many dimensions we create, addind an additional point renders an impossible situation - or an 'unoccupiable space', which means any dimensional space has the potential of being unoccuiable because a limited number of points can form vertices of a simplex.


So, in any space, there is a place which inherently unoccupied due to its dimensional constraint.