All Questions

Let $G$ be a finite (not necessarily abelian) group. We call $A \subseteq G$ a right-tiling (for simplicity, a tiling) of $G$ if there exists a $B \subseteq G$ so that $$ G = \bigsqcup_{b\in B} bA.$$ ...

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. ...