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http://hdl.handle.net/10773/32946| Title: | Packing of R3 by crosses |
| Author: | Cruz, Catarina M. N. Breda, Ana M. D'Azevedo |
| Keywords: | Packing Tiling Lattice Cross Homomorphism Abelian group |
| Issue Date: | 2019 |
| Publisher: | Association for Computing Machinery (ACM) |
| Abstract: | The existence of tilings of R^n by crosses, a cluster of unit cubes comprising a central one and 2n arms, has been studied by several
authors. We have completely solved the problem for R^2, characterizing the crosses which lattice tile R^2, as well as determining the maximum packing density for the crosses which do not lattice tile the plane. In this paper we motivate a similar approach to study lattice packings of R^3 by crosses. The existence of tilings of Rn by crosses, a cluster of unit cubes comprising a central one and 2n arms, has been studied by several authors. We have completely solved the problem for R2 characterizing the crosses which lattice tile R2 as well as determining the maximum packing density for the crosses which do not lattice tile the plane. In this paper we motivate a similar approach to study lattice packings of R3 by crosses. |
| Peer review: | yes |
| URI: | http://hdl.handle.net/10773/32946 |
| DOI: | 10.1145/3343485.3343502 |
| ISBN: | 978-1-4503-7168-1 |
| Appears in Collections: | CIDMA - Capítulo de livro AGG - Capítulo de livro |
Files in This Item:
| File | Description | Size | Format | |
|---|---|---|---|---|
| pckingcrosses.pdf | 792.8 kB | Adobe PDF | View/Open |
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