Uniform partitions of 3-space, their relatives and embedding

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dc.creatorDeza, M.
dc.creatorShtogrin, M. I.
dc.date1999-06-06
dc.date.accessioned2026-07-07T05:29:23Z
dc.date.available2026-07-07T05:29:23Z
dc.descriptionWe review 28 uniform partitions of 3-space in order to find out which of them have graphs (skeletons) embeddable isometrically (or with scale 2) into some cubic lattice ${\bf Z}_n$. We also consider some relatives of those 28 partitions, including Achimedean 4-polytopes of Conway-Guy, non-compact uniform partitions, Kelvin partitions and those with unique vertex figure (i.e. Delaunay star). Among last ones we indicate two continuums of aperiodic tilings by semi-regular 3-prisms with cubes or with regular tetrahedra and regular octahedra. On the way many new partitions are added to incomplete cases considered here.
dc.description11 pages
dc.identifierhttps://arxiv.org/abs/math/9906034
dc.identifierhttp://arxiv.org/abs/math/9906034
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/78617
dc.subjectMetric Geometry
dc.subjectCombinatorics
dc.titleUniform partitions of 3-space, their relatives and embedding
dc.typetext

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