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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