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< Again, begin with the simplest figure: a 4D hypersphere (a.k.a. glome). Somewhat unintuitively to non-mathematicians, this is also termed a 3-sphere.
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> Again, begin with the simplest figure: a 4D hypersphere (a.k.a. glome). Somewhat unintuitively to non-mathematicians, this is also termed a 3-sphere, because any point on its "surface" can be specified with three coordinates. (The familiar 3D sphere, such as a globe of the Earth, is called a 2-sphere for analogous reasons; you can specify any point on its surface with only lines of latitude and longitude.)
A brief outline with some thoughts to flesh out....
For 4D objects, begin with the tesseract (or 4D hypercube, the 4D analog of a cube) and the pentachoron (or 4-simplex, the 4D analog of a tetrahedron).
Again, begin with the simplest figure: a 4D hypersphere (a.k.a. glome). Somewhat unintuitively to non-mathematicians, this is also termed a 3-sphere, because any point on its "surface" can be specified with three coordinates. (The familiar 3D sphere, such as a globe of the Earth, is called a 2-sphere for analogous reasons; you can specify any point on its surface with only lines of latitude and longitude.)