Or is that a quirk of trying to reproduce it on a 2-D surface trying to reproduce a 3-D analogy?
A hypercube can be any size (hypervolume, technically) but to answer your question, it’s the 3D or 2D slice of the hypercube that changes volume or area, respectively.
It’s actually easier to see with a hypersphere:
First, think of slicing a sphere into circles, you’ll start with small ones, get bigger circles very quickly, and then the size of the circles still increases but more slowly, until they reach a circle with the same radius as the sphere, then slowly start to decrease again and then speed up the decrease until it’s small circles again. Did that make sense?
A hypersphere sliced into spheres is the same: Smaller spheres that get bigger quickly, then slow, reach the largest size sphere with the same radius as the hypersphere, decrease, decrease faster, end with small sphere again.
The same effect happens when slicing any hypervolume.
Are there examples of hypervolumes in real life/reified?
How are they applied or to what end are they useful beyond the purely mathematical?
That’s a tricky question! But it is mostly used in purely mathematical contexts currently. Though, as with so much of pure math, we don’t always know in advance what will end up being useful in the material world.
