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The contraction types of parallelohedra in $$E^5$$. (English) Zbl 1188.52021
Summary: Using the process of zone contraction and its inverse, zone extension, the $$179\,372$$ contraction types of parallelohedra in $$E^5$$ are derived from the 84 combinatorial types of relatively or totally zone-contracted parallelohedra.

##### MSC:
 52C22 Tilings in $$n$$ dimensions (aspects of discrete geometry) 52B99 Polytopes and polyhedra 82D25 Statistical mechanics of crystals
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