Geometry in higher dimensions is not only hard to imagine, it's straight up weird.
Take a cube on N dimensions and pack N dimensional spheres inside that cube. Then fit a sphere inside the cube so that it touches but doesn't overlap with any of the other spheres.
In 2D and 3D is easy to visualize and you can see that sphere in the center is smaller than the other spheres and of course it's smaller than the cube itself; after all, it's surrounded by the other spheres that are by construction inside the cube.
Above 10 dimensions the size of the inner hypersphere is actually bigger than the size of the hypercube despite being surrounded by hyperspheres that are contained inside the hyper-cube!
The math behind it is straightforward but the implication is as counterintuitive as it gets
Take a cube on N dimensions and pack N dimensional spheres inside that cube. Then fit a sphere inside the cube so that it touches but doesn't overlap with any of the other spheres.
In 2D and 3D is easy to visualize and you can see that sphere in the center is smaller than the other spheres and of course it's smaller than the cube itself; after all, it's surrounded by the other spheres that are by construction inside the cube.
Above 10 dimensions the size of the inner hypersphere is actually bigger than the size of the hypercube despite being surrounded by hyperspheres that are contained inside the hyper-cube!
The math behind it is straightforward but the implication is as counterintuitive as it gets