✦ LIBER ✦

Uniform Partitions of 3-space, their Relatives and Embedding

✍ Scribed by Michel Deza; Mikhail Shtogrin

Publisher: Elsevier Science
Year: 2000
Tongue: English
Weight: 102 KB
Volume: 21
Category: Article
ISSN: 0195-6698
DOI: 10.1006/eujc.1999.0385

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✦ Synopsis

We 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 Z n . We also consider some relatives of those 28 partitions, including Archimedean 4-polytopes of Conway-Guy, non-compact uniform partitions, Kelvin partitions and those with a unique vertex figure (i.e., Delaunay star). Among the latter ones we indicate two continuums of aperiodic tilings by semi-regular 3-prisms with cubes or with regular tetrahedra and regular octahedra. In the process many new partitions are added to the incomplete cases considered here.

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