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Suppose that we have a tiling of $n$-dimensional (I want to get answer for $n = 4$, but general result would be nice!) sphere by isometric tiles strictly contained inside the right-angled simplex. What is the set of possible numbers of tiles? There is an obvious restriction on the highest prime divisor coming from Jordan number of $SO(n)$, but is it the only real one?

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    $\begingroup$ Interesting question. What is this Jordan number? $\endgroup$
    – M. Winter
    Commented Nov 16, 2020 at 9:03

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