r/Geometry • u/Spluff5 • 21d ago

Angles of a 4D Hypercube

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Stereographic projection of a 4-dimensional hypercube (tesseract) with axes labeled a-d, and all six right-angles labelled according to standard crystallographic conventions.

Art by me, Inkscape

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u/Ok-Rise2070 17d ago

If this is a hypercube, a slice of the hypersphere, how do you account for the lack of curvature in your model? The axes of expansion warp the straight lines of the hypercube so what normalization technique do you apply in your derivations?

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u/Spluff5 17d ago

What do you mean the hypercube is a slice of a hypersphere?

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u/Ok-Rise2070 13d ago

Reality is built off the hypersphere. Any other hyper shape is a fraction of that hypersphere as a whole. Knowing that, you can also express the hypercube as the hypersphere equations minus the areas cut off. This preserves the full curvature of the hypercube.