Also, in 4096-d the intersection of hyperspherical shells won’t have a toroidal topology, but rather something considerably more exotic.
The intersection of two hyperspheres is another hypersphere (1-d lower).
So I guess the intersection of two thick/fuzzy hyperspheres is a thick/fuzzy hypersphere (1-d lower). Note that your ‘torus’ is also described as thick/fuzzy circle (aka 1-sphere), which fits this pattern.
The intersection of two hyperspheres is another hypersphere (1-d lower).
So I guess the intersection of two thick/fuzzy hyperspheres is a thick/fuzzy hypersphere (1-d lower). Note that your ‘torus’ is also described as thick/fuzzy circle (aka 1-sphere), which fits this pattern.