It is shown here that, for $n \geq 2$, the $n$-torus is the only $n$-dimensional compact euclidean space-form which can admit a regular or chiral tessellation. Further, such a tessellation can only be chiral if $n = 2$.

Keywords:

polyhedra and polytopes, regular figures, division of space polyhedra and polytopes, regular figures, division of space

MSC Classifications:

51M20 show english descriptions Polyhedra and polytopes; regular figures, division of spaces [See also 51F15] 51M20 - Polyhedra and polytopes; regular figures, division of spaces [See also 51F15]

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