This list of spacial concepts will more likely help the foxes rather than the hedgehogs.
Foxes like fox a top down approach to understanding the universe including its mathematical underpinings.
This is the approach to mathematics taken by Terence Tao, Fields medalist, and professor of mathematics among others.
Mathematics has evolved over time. It is "of this world" which means it has evolved in the context of our human sensory limits, and then progressively, through our instrumentation enabled experimentation. Mathematics has been challenged by human problems and the physics of the world and evolved directly as a result of those challenges.
The unreasonable effectiveness of mathematics in the natural sciences" by Eugene Wigner (1960 Communications in Pure and Applied Mathematics) explores this mystifying problem.
The standard 6 parameter cosmological-constant (Lambda - Λ) model of the universe, the Cold Dark Matter (CDM) model has been successfully aligned with large array of cosmological observations.
Central to mathematics has been the essence of space. Successive definitions of space have given us new tools for understanding the nature of reality and for computational progress.
Geometry is a branch of mathematics concerned with properties of space such as the distance, shape, size, and relative position of figures. It has a very long and distiguished history".
Here is a 12 min review of modern geometry
