The solids **do not intersect**. Their minimum surface separation is **0.012132 m (about 12.13 mm)**.

The oriented-box **separating axis test (SAT)** finds a gap along their shared width direction, \((-1/\sqrt{2},\,1/\sqrt{2},\,0)\). The centre separation projected onto this axis is \(0.30/\sqrt{2}=0.212132\) m. Their combined half-widths are \(0.10+0.10=0.20\) m, leaving:

\[
g=\frac{0.30}{\sqrt{2}}-0.20=0.012132\text{ m}.
\]

Their extents overlap along the length and Z directions, so this width-direction gap is also the minimum surface separation.