### A stability theorem on cube tessellations

#### Abstract

It is shown that if a $d$-dimensional cube is decomposed into $n$ cubes, the side lengths

of which belong to the interval $(1 − \frac{n}{1/d 1 +1} , 1]$, then $n$ is a perfect $d$-th power and all

cubes are of the same size. This result is essentially tight.

#### Full Text:

PDFDOI: http://dx.doi.org/10.20382/jocg.v9i1a13

ISSN: 1920-180X