𝔖 Bobbio Scriptorium
✦   LIBER   ✦

Tiling space with notched cubes

✍ Scribed by James H. Schmerl


Publisher
Elsevier Science
Year
1994
Tongue
English
Weight
729 KB
Volume
133
Category
Article
ISSN
0012-365X

No coin nor oath required. For personal study only.

✦ Synopsis


Stein (1990)

discovered (n -l)! lattice tilings of R" by translates of the notched n-cube which are inequivalent under translation. We show that there are no other inequivalent tilings of IF!" by translates of the notched cube.


πŸ“œ SIMILAR VOLUMES


The notched cube tiles Rn
✍ Sherman Stein πŸ“‚ Article πŸ“… 1990 πŸ› Elsevier Science 🌐 English βš– 191 KB

Herb Holden once observed that packing material consisting of copies of a cube of side 2 inches from which a unit corner cube is removed tiles R3 by translates. In [l] Conlan generalized this fact, proving that a polytope obtained from a unit cube in R3 by deleting a corner box of which two dimensio

Tiling Hamming Space with Few Spheres
✍ Henk D.L Hollmann; JΓ‘nos KΓΆrner; Simon Litsyn πŸ“‚ Article πŸ“… 1997 πŸ› Elsevier Science 🌐 English βš– 272 KB

We show that if the collection of all binary vectors of length n is partitioned into k spheres, then either k 2 or k n+2. Moreover, such partitions with k=n+2 are essentially unique. ## 1997 Academic Press Recently there has been some interest in the combinatorics of the geometry of the Hamming sp