In 1984 Shechtman et al. [lo] discovered alloys with a novel kind of structure, intermediate between crystalline and amorphous. These alloys, called qruzskrystuk [8], exhibit long-range orientational order but no translational symmetry. Since fivefold and even icosahedral symmetry is observed, seve
✦ LIBER ✦
The inflation pattern of the three-dimensional Penrose tiling
✍ Scribed by Reinhard Lück
- Publisher
- Elsevier Science
- Year
- 1991
- Tongue
- English
- Weight
- 244 KB
- Volume
- 134
- Category
- Article
- ISSN
- 0921-5093
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We prove that there does not exist a tiling with Lee spheres of radius at least 2 in the 3-dimensional Euclidean space. In particular, this result verifies a conjecture of Golomb and Welch for n = 3.