The open problem of covering k-dimensional space with laice translates of
a simplex as efficiently as possible is related to the problem of generating a
finite Abelian group with k generators and with shortest possible maximum
word-length. For k≥3 the best answer is not known, but it leads into many
interesting corners of mathematics — calculus, combinatorics, convexity,
groups, even a lile algebraic geometry.
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