Reserve in packing cubes into the unit cube
Volume 71 / 2023
Bulletin Polish Acad. Sci. Math. 71 (2023), 85-95
MSC: Primary 52C17; Secondary 52C15.
DOI: 10.4064/ba230215-21-6
Published online: 29 June 2023
Abstract
Any collection of $d$-dimensional cubes of total volume not greater than $2^{1-d}$ can be packed into the unit $d$-dimensional cube $I^d$ so that the uncovered part of $I^d$ contains a cube of edge length $1-\sqrt[d]{2}/2$. To achieve this result, the well-known packing method described by Meir and Moser is used.
