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John Baez Mastodon
Here's some crazy geometry in 4, 5 and 6 dimensions: The 4-demicube has 8 vertices. It lives in 4 dimensions. You get it from a 4-dimensional cube - which has 16 vertices - by keeping every other vertex, throwing away half. That leaves 8. What are its top-dimensional faces, aka 'facets'? Surprise: there's only one kind! All of them are regular tetrahedra. In higher dimensions the demicube has two kinds of facet - one from the cube's corners, one from the cube's facets. But in 4 dimensions the two kinds happen to be the same shape: the tetrahedron! That's why the 4-demicube is especially symme…
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