The hypersphere can be decomposed into two solid toripic.twitter.com/zZMeEiWCH0
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You say hyperSPHERE and SOLID tori, so the two filled tori would be composing the SURFACE of a hyper-ball. I really don't get how though, is there a close analog of this in 2 and 3 dimensions?
A hypersphere is 3 dimensional, and so is a solid torus. You might be confused by the fact that one is embedded in 4d and one in 3d. An ordinary sphere (2d surface in 3d space) can be cut into two discs (filled-in circles, 2d living in 2d).
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I see. Since a hypersphere is the 3D surface of a shape that exists in 4 dimensions, 3D shapes can "live inside" it (like how flatlanders could live "inside" a torus surface or mobius strip) https://youtu.be/-gLNlC_hQ3M One of the two solid torii is the outside of the other, i see
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that is mindblowing, I do see now though. I'm already familiar with 3-torus (4D shape 3D surface) as a 3-manifold and how it createds the weird infinite repeating effect, and triangles with 3 right angles existing on a sphere surface and how it relates to noneuclidian tilings etc
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