Given two points in space, we define a geodesic as the line of shortest length spanning the space between the two points. The Dimension of Space. For example, in the trivial case of a one-dimensional space, only two points can be mutually equidistant. For a two-dimensional space, no more than three points can be mutually equidistant. For a three-dimensional space, no more than four points can be mutually equidistant.
Physical space is three-dimensional.
Why space is so limited we do not know. This property does not seem to derive from any other character of space or from other laws of physics. The geometry of space is embodied in the set of postulates which govern the relationships among geometric figures constructed from points and lines and curves lying the space. From these postulates, the properties of space may be derived under logical and mathematically rigorous methods. That nature yields measures in agreement with these predictions is both the faith and foundation of all science.