We prove that for an arbitrary $\varepsilon > 0$ holds \[ χ(\mathbb{R}^3 \times [0,\varepsilon]^6) \geq 10, \] where $χ(M)$ stands for the chromatic number of an (infinite) graph with the vertex set $M$ and the edge set consists of pairs of monochromatic points at the distance 1 apart.
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