The DOI matches its Crossref record; 11 of the 11 references it cites were found in a registry or an index.
A highly symmetric four-dimensional quasicrystal
Open accessAbstract
A quasiperiodic pattern (or quasicrystal) is constructed in real four-dimensional Euclidean space, having the non-crystallographic reflection group (3, 3, 5) of order 14 400 as its point group. It is obtained as a projection of the eight-dimensional lattice E 8 , and has as a cross section a three-dimensional quasicrystal with icosahedral symmetry.
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“Notably, the FIG bears a striking resemblance to a 3D quasicrystal that composites five 3D slices of the Elser-Sloane quasicrystal found from the E 8 lattice via the cut-and-project method [29].”
From From the Fibonacci Icosagrid to E8 (Part I): The Fibonacci Icosagrid, an H3 Quasicrystal (2024) · cites this paper as [29]
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“As a matter of fact, we discovered that the FIG is very similar to a 3D quasicrystal that is a golden composition of a 5 or 20 3D tetrahedral (T 3 ) slice of the ESQC [29] (a 4D quasicrystal cut and projected from the E 8 lattice).”
From From the Fibonacci Icosagrid to E8 (Part I): The Fibonacci Icosagrid, an H3 Quasicrystal (2024) · cites this paper as [29]
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Citations
Cites
Sphere Packings, Lattices and Groups.
Coxeter, H. S. M., Conway, J. H., & Sloane, N. J. A. (1989) · American Mathematical Monthly · doi:10.2307/2323992 · Cited by 3,373
Self-citationGenerators and Relations for Discrete Groups
Coxeter, H. S. M., & Moser, W. O. J. (1972) · Springer eBooks · doi:10.1007/978-3-662-21946-1 · Cited by 1,506
Duneau, M., & Katz, A. (1985) · Physical Review Letters · doi:10.1103/physrevlett.54.2688 · Cited by 594
The diffraction pattern of projected structures
Elser, V. (1986) · Acta Crystallographica Section A Foundations of Crystallography · doi:10.1107/s0108767386099932 · Cited by 417
Self-citationOn periodic and non-periodic space fillings of Emobtained by projection
Kramer, P., & Neri, R. (1984) · Acta Crystallographica Section A Foundations of Crystallography · doi:10.1107/s0108767384001203 · Cited by 396
Voronoi regions of lattices, second moments of polytopes, and quantization
Conway, J., & Sloane, N. J. A. (1982) · IEEE Transactions on Information Theory · doi:10.1109/tit.1982.1056483 · Cited by 325
Self-citationQuasiperiodic patterns and icosahedral symmetry
Katz, A., & Duneau, M. (1986) · Journal de physique · doi:10.1051/jphys:01986004702018100 · Cited by 295
Sphere Packings and Error-Correcting Codes
Leech, J., & Sloane, N. J. A. (1971) · Canadian Journal of Mathematics · doi:10.4153/cjm-1971-081-3 · Cited by 202
Self-citationHomographies, Quaternions, and Rotations.
Scherk, P., & Val, P. D. (1966) · American Mathematical Monthly · doi:10.2307/2314230 · Cited by 197
Burn, R. P. (1985) · Cambridge University Press eBooks · doi:10.1017/cbo9781139163590.020 · Cited by 75
Research works printed but not linked: 1
- de Bruijn N G, 1981, Proc. K. Ned. Akad. Wet., 43, 39
Cited by
Sorted by citations
Fang, F., & Irwin, K. (2015) · arXiv · doi:10.48550/arxiv.1511.07786 · Cited by 12
Fang, F., Clawson, R., & Irwin, K. (2018) · Mathematics · doi:10.3390/math6060089 · Cited by 5
From the Fibonacci Icosagrid to E8 (Part I): The Fibonacci Icosagrid, an H3 Quasicrystal
Fang, F., & Irwin, K. (2024) · Crystals · doi:10.3390/cryst14020152 · Cited by 1
Metadata
- Authors
- Elser, V, & Sloane, N. J. A.
- Affiliations
- AT&T (United States) (US)
- Venue
- Journal of Physics A: Mathematical and General
- Publisher
- IOP Publishing
- Published
- 1987-12-21
- Volume
- 20
- Issue
- 18
- Pages
- 6161-6167
- ISSN
- 0305-4470 (ISSN-L)
- 1361-6447
- OpenAlex
- W2102586619
- Cited by
- 57
- References
- 11
- Citations by year
- 2025: 2 · 2024: 3 · 2022: 2 · 2021: 3 · 2019: 6 · 2018: 1 · 2016: 1 · 2015: 1 · 2014: 2 · 2013: 1 · 2012: 1
- FWCI
- 0.93
- Type
- journal article
- Language
- en
- Open access
- bronze
- doi.org
- Locations
- Journal of Physics A Mathematical and General (publishedVersion)
- Topics
- Physical Sciences › Materials Science › Materials Chemistry › Quasicrystal Structures and Properties
- Physical Sciences › Physics and Astronomy › Statistical and Nonlinear Physics › Advanced Mathematical Theories and Applications
- Physical Sciences › Mathematics › Geometry and Topology › Mathematics and Applications
- Keywords
- quasicrystals, quasiperiodic patterns, E8 lattice, icosahedral symmetry, projection method, point groups
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